From 5884ff68004165f36dbc15825bfaa6e3252027e5 Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 12:01:20 -0300
Subject: [PATCH 01/25] chore: print ACIR AssertZero as an equation

---
 acvm-repo/acir/src/circuit/mod.rs             |   2 +-
 acvm-repo/acir/src/circuit/opcodes.rs         |  37 +++-
 acvm-repo/acir/src/parser/lexer.rs            |   3 +
 acvm-repo/acir/src/parser/mod.rs              |  73 ++++++-
 acvm-repo/acir/src/parser/tests.rs            | 206 +++++++++---------
 acvm-repo/acir/src/parser/token.rs            |   9 +
 .../acvm/src/compiler/optimizers/general.rs   |  12 +-
 .../compiler/optimizers/merge_expressions.rs  |   4 +-
 .../compiler/optimizers/redundant_range.rs    |  12 +-
 .../noirc_evaluator/src/acir/tests/arrays.rs  |  72 +++---
 .../src/acir/tests/brillig_call.rs            |  58 ++---
 .../noirc_evaluator/src/acir/tests/call.rs    |  30 +--
 .../noirc_evaluator/src/acir/tests/mod.rs     |   2 +-
 13 files changed, 317 insertions(+), 203 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/mod.rs b/acvm-repo/acir/src/circuit/mod.rs
index 35b8f7440dd..1dd1e2f8bb0 100644
--- a/acvm-repo/acir/src/circuit/mod.rs
+++ b/acvm-repo/acir/src/circuit/mod.rs
@@ -544,7 +544,7 @@ mod tests {
         private parameters: []
         public parameters: [w2]
         return values: [w2]
-        EXPR [ (2, w1) 8 ]
+        EXPR 2*w1 + 8 = 0
         BLACKBOX::RANGE [w1]:8 bits []
         BLACKBOX::AND [w1, w2]:4 bits [w3]
         BLACKBOX::KECCAKF1600 [w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25] [w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43, w44, w45, w46, w47, w48, w49, w50]
diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index f8962bad9bf..3a169e535f2 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -146,16 +146,47 @@ pub enum Opcode<F: AcirField> {
 impl<F: AcirField> std::fmt::Display for Opcode<F> {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         match self {
-            Opcode::AssertZero(expr) => expr.fmt(f),
+            Opcode::AssertZero(expr) => {
+                write!(f, "EXPR ")?;
+
+                let mut printed_term = false;
+
+                for (coefficient, witness1, witness2) in &expr.mul_terms {
+                    if printed_term {
+                        write!(f, " + ")?;
+                    }
+
+                    write!(f, "{coefficient}*{witness1}*{witness2}")?;
+                    printed_term = true;
+                }
+
+                for (coefficient, witness) in &expr.linear_combinations {
+                    if printed_term {
+                        write!(f, " + ")?;
+                    }
+
+                    write!(f, "{coefficient}*{witness}")?;
+                    printed_term = true;
+                }
+
+                if printed_term {
+                    write!(f, " + ")?;
+                }
+
+                write!(f, "{}", expr.q_c)?;
+                write!(f, " = 0")?;
+
+                Ok(())
+            }
             Opcode::BlackBoxFuncCall(g) => g.fmt(f),
             Opcode::MemoryOp { block_id, op } => {
                 write!(f, "MEM ")?;
 
                 let is_read = op.operation.is_zero();
                 if is_read {
-                    write!(f, "(id: {}, read at: {}, value: {}) ", block_id.0, op.index, op.value)
+                    write!(f, "(id: {}, read at: {}, value: {})", block_id.0, op.index, op.value)
                 } else {
-                    write!(f, "(id: {}, write {} at: {}) ", block_id.0, op.value, op.index)
+                    write!(f, "(id: {}, write {} at: {})", block_id.0, op.value, op.index)
                 }
             }
             Opcode::MemoryInit { block_id, init, block_type: databus } => {
diff --git a/acvm-repo/acir/src/parser/lexer.rs b/acvm-repo/acir/src/parser/lexer.rs
index 4049980789c..c30b5badbd7 100644
--- a/acvm-repo/acir/src/parser/lexer.rs
+++ b/acvm-repo/acir/src/parser/lexer.rs
@@ -64,6 +64,9 @@ impl<'a> Lexer<'a> {
             ',' => self.single_char_token(Token::Comma),
             ':' => self.single_char_token(Token::Colon),
             ';' => self.single_char_token(Token::Semicolon),
+            '+' => self.single_char_token(Token::Plus),
+            '*' => self.single_char_token(Token::Star),
+            '=' => self.single_char_token(Token::Equal),
             'w' if self.peek_char().is_some_and(|char| char.is_ascii_digit()) => {
                 let start = self.position;
 
diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index 0325d7f7c98..2fe2deb6323 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -235,7 +235,7 @@ impl<'a> Parser<'a> {
         while let Some(keyword) = self.peek_keyword() {
             match keyword {
                 Keyword::Expression => {
-                    let expr = self.parse_arithmetic_expression()?;
+                    let expr = self.parse_assert_zero_expression()?;
                     opcodes.push(Opcode::AssertZero(expr));
                 }
                 Keyword::BlackBoxFuncCall => {
@@ -260,8 +260,76 @@ impl<'a> Parser<'a> {
         Ok(opcodes)
     }
 
+    fn parse_assert_zero_expression(&mut self) -> ParseResult<Expression<FieldElement>> {
+        self.eat_keyword_or_error(Keyword::Expression)?;
+
+        // Support the old `EXPR [ ... ]` syntax for old tests, for now
+        if matches!(self.token.token(), Token::LeftBracket) {
+            return self.parse_arithmetic_expression_after_expr();
+        }
+
+        let mut linear_combinations = Vec::new();
+        let mut mul_terms = Vec::new();
+        let mut constant: Option<FieldElement> = None;
+
+        loop {
+            let Some(coefficient) = self.eat_field_element()? else {
+                return self.expected_field_element();
+            };
+
+            if self.eat(Token::Star)? {
+                let w1 = self.eat_witness_or_error()?;
+
+                if self.eat(Token::Star)? {
+                    let w2 = self.eat_witness_or_error()?;
+                    mul_terms.push((coefficient, w1, w2));
+                } else {
+                    linear_combinations.push((coefficient, w1));
+                }
+            } else {
+                if constant.is_some() {
+                    return Err(ParserError::DuplicatedConstantTerm {
+                        found: self.token.token().clone(),
+                        span: self.token.span(),
+                    });
+                }
+                constant = Some(coefficient);
+            }
+
+            if self.eat(Token::Plus)? {
+                continue;
+            }
+
+            if self.eat(Token::Equal)? {
+                break;
+            }
+
+            return self.expected_token(Token::Equal);
+        }
+
+        let zero_token = self.token.token().clone();
+        let span = self.token.span();
+        let Some(zero) = self.eat_field_element()? else {
+            return self.expected_field_element();
+        };
+
+        if !zero.is_zero() {
+            return Err(ParserError::ExpectedZero { found: zero_token, span });
+        }
+
+        let Some(q_c) = constant else {
+            return Err(ParserError::MissingConstantTerm { span: self.token.span() });
+        };
+
+        Ok(Expression { mul_terms, linear_combinations, q_c })
+    }
+
     fn parse_arithmetic_expression(&mut self) -> ParseResult<Expression<FieldElement>> {
         self.eat_keyword_or_error(Keyword::Expression)?;
+        self.parse_arithmetic_expression_after_expr()
+    }
+
+    fn parse_arithmetic_expression_after_expr(&mut self) -> ParseResult<Expression<FieldElement>> {
         self.eat_or_error(Token::LeftBracket)?;
 
         let mut linear_combinations = Vec::new();
@@ -1014,6 +1082,8 @@ pub(crate) enum ParserError {
     ExpectedFieldElement { found: Token, span: Span },
     #[error("Expected a witness index, found '{found}'")]
     ExpectedWitness { found: Token, span: Span },
+    #[error("Expected a zero, found '{found}'")]
+    ExpectedZero { found: Token, span: Span },
     #[error("Duplicate constant term in native Expression")]
     DuplicatedConstantTerm { found: Token, span: Span },
     #[error("Missing constant term in native Expression")]
@@ -1042,6 +1112,7 @@ impl ParserError {
             | ExpectedIdentifier { span, .. }
             | ExpectedFieldElement { span, .. }
             | ExpectedWitness { span, .. }
+            | ExpectedZero { span, .. }
             | DuplicatedConstantTerm { span, .. }
             | MissingConstantTerm { span }
             | ExpectedBlackBoxFuncName { span, .. }
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index d6a13336af2..f28a2a9eb85 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -102,11 +102,11 @@ fn assert_zero_opcodes() {
     private parameters: [w0, w1, w2, w3, w4]
     public parameters: [w5, w6, w7, w8, w9]
     return values: []
-    EXPR [ (1, w0) (-1, w5) 0 ]
-    EXPR [ (1, w1) (-1, w6) 0 ]
-    EXPR [ (1, w2) (-1, w7) 0 ]
-    EXPR [ (1, w3) (-1, w8) 0 ]
-    EXPR [ (1, w4) (-1, w9) 0 ]    
+    EXPR 1*w0 + -1*w5 + 0 = 0
+    EXPR 1*w1 + -1*w6 + 0 = 0
+    EXPR 1*w2 + -1*w7 + 0 = 0
+    EXPR 1*w3 + -1*w8 + 0 = 0
+    EXPR 1*w4 + -1*w9 + 0 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -118,11 +118,11 @@ fn assert_zero_with_mul_terms() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    EXPR [ (1, w0, w1) (-1, w3) 0 ]
-    EXPR [ (1, w3, w3) (-1, w4) 0 ]
-    EXPR [ (1, w4, w4) (-1, w5) 0 ]
-    EXPR [ (1, w5, w5) (-1, w6) 0 ]
-    EXPR [ (-1, w2) (1, w6) 0 ]
+    EXPR 1*w0*w1 + -1*w3 + 0 = 0
+    EXPR 1*w3*w3 + -1*w4 + 0 = 0
+    EXPR 1*w4*w4 + -1*w5 + 0 = 0
+    EXPR 1*w5*w5 + -1*w6 + 0 = 0
+    EXPR -1*w2 + 1*w6 + 0 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -149,7 +149,7 @@ fn xor() {
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::XOR [w0, w1]:32 bits [w2]
-    EXPR [ (1, w2) -15 ]
+    EXPR 1*w2 + -15 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -223,22 +223,22 @@ fn aes128_encrypt() {
     BLACKBOX::RANGE [w58]:8 bits []
     BLACKBOX::RANGE [w59]:8 bits []
     BLACKBOX::AES128_ENCRYPT [w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43] [w60, w61, w62, w63, w64, w65, w66, w67, w68, w69, w70, w71, w72, w73, w74, w75]
-    EXPR [ (-1, w44) (1, w60) 0 ]
-    EXPR [ (-1, w45) (1, w61) 0 ]
-    EXPR [ (-1, w46) (1, w62) 0 ]
-    EXPR [ (-1, w47) (1, w63) 0 ]
-    EXPR [ (-1, w48) (1, w64) 0 ]
-    EXPR [ (-1, w49) (1, w65) 0 ]
-    EXPR [ (-1, w50) (1, w66) 0 ]
-    EXPR [ (-1, w51) (1, w67) 0 ]
-    EXPR [ (-1, w52) (1, w68) 0 ]
-    EXPR [ (-1, w53) (1, w69) 0 ]
-    EXPR [ (-1, w54) (1, w70) 0 ]
-    EXPR [ (-1, w55) (1, w71) 0 ]
-    EXPR [ (-1, w56) (1, w72) 0 ]
-    EXPR [ (-1, w57) (1, w73) 0 ]
-    EXPR [ (-1, w58) (1, w74) 0 ]
-    EXPR [ (-1, w59) (1, w75) 0 ]
+    EXPR -1*w44 + 1*w60 + 0 = 0
+    EXPR -1*w45 + 1*w61 + 0 = 0
+    EXPR -1*w46 + 1*w62 + 0 = 0
+    EXPR -1*w47 + 1*w63 + 0 = 0
+    EXPR -1*w48 + 1*w64 + 0 = 0
+    EXPR -1*w49 + 1*w65 + 0 = 0
+    EXPR -1*w50 + 1*w66 + 0 = 0
+    EXPR -1*w51 + 1*w67 + 0 = 0
+    EXPR -1*w52 + 1*w68 + 0 = 0
+    EXPR -1*w53 + 1*w69 + 0 = 0
+    EXPR -1*w54 + 1*w70 + 0 = 0
+    EXPR -1*w55 + 1*w71 + 0 = 0
+    EXPR -1*w56 + 1*w72 + 0 = 0
+    EXPR -1*w57 + 1*w73 + 0 = 0
+    EXPR -1*w58 + 1*w74 + 0 = 0
+    EXPR -1*w59 + 1*w75 + 0 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -463,7 +463,7 @@ fn memory_read() {
     private parameters: []
     public parameters: []
     return values: []
-    MEM (id: 0, read at: EXPR [ (1, w0) 0 ], value: EXPR [ (1, w1) 0 ]) 
+    MEM (id: 0, read at: EXPR [ (1, w0) 0 ], value: EXPR [ (1, w1) 0 ])
     ";
     assert_circuit_roundtrip(src);
 }
@@ -525,8 +525,8 @@ fn brillig_call() {
     public parameters: []
     return values: []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
-    EXPR [ (1, w0, w3) (-1, w1, w3) -1 ]
-    EXPR [ (-1, w0) (1, w2) 0 ]
+    EXPR 1*w0*w3 + -1*w1*w3 + -1 = 0
+    EXPR -1*w0 + 1*w2 + 0 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -540,8 +540,8 @@ fn brillig_call_with_predicate() {
     return values: []
     BRILLIG CALL func 0: PREDICATE: EXPR [ 1 ]
     inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
-    EXPR [ (1, w0, w3) (-1, w1, w3) -1 ]
-    EXPR [ (-1, w0) (1, w2) 0 ]
+    EXPR 1*w0*w3 + -1*w1*w3 + -1 = 0
+    EXPR -1*w0 + 1*w2 + 0 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -606,97 +606,97 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w15]:32 bits []
     BLACKBOX::RANGE [w16]:32 bits []
     BLACKBOX::RANGE [w17]:32 bits []
-    EXPR [ (5, w6) (-1, w19) 0 ]
+    EXPR 5*w6 + -1*w19 + 0 = 0
     BLACKBOX::RANGE [w19]:32 bits []
-    EXPR [ (1, w5) (-1, w19) (-1, w20) 0 ]
+    EXPR 1*w5 + -1*w19 + -1*w20 + 0 = 0
     BLACKBOX::RANGE [w20]:32 bits []
-    EXPR [ (1, w20) (-1, w21) -5 ]
-    EXPR [ (1, w21) (-1, w22) -3 ]
-    MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w23) 0 ]) 
-    EXPR [ (1, w23) -111 ]
-    MEM (id: 0, read at: EXPR [ (1, w22) 0 ], value: EXPR [ (1, w24) 0 ]) 
-    EXPR [ (1, w24) -101 ]
+    EXPR 1*w20 + -1*w21 + -5 = 0
+    EXPR 1*w21 + -1*w22 + -3 = 0
+    MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w23) 0 ])
+    EXPR 1*w23 + -111 = 0
+    MEM (id: 0, read at: EXPR [ (1, w22) 0 ], value: EXPR [ (1, w24) 0 ])
+    EXPR 1*w24 + -101 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w22) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w25, w26]
     BLACKBOX::RANGE [w26]:32 bits []
-    EXPR [ (1, w22) (-4294967296, w25) (-1, w26) 4294967291 ]
-    EXPR [ (-1, w25) 0 ]
-    EXPR [ (-1, w27) 0 ]
-    MEM (id: 0, write EXPR [ (1, w27) 0 ] at: EXPR [ (1, w22) 0 ]) 
-    MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w28) 0 ]) 
-    EXPR [ (1, w28) -111 ]
-    EXPR [ (-1, w29) 1 ]
-    MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w30) 0 ]) 
-    EXPR [ (1, w30) 0 ]
+    EXPR 1*w22 + -4294967296*w25 + -1*w26 + 4294967291 = 0
+    EXPR -1*w25 + 0 = 0
+    EXPR -1*w27 + 0 = 0
+    MEM (id: 0, write EXPR [ (1, w27) 0 ] at: EXPR [ (1, w22) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w28) 0 ])
+    EXPR 1*w28 + -111 = 0
+    EXPR -1*w29 + 1 = 0
+    MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w30) 0 ])
+    EXPR 1*w30 + 0 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967286 ], EXPR [ 4294967296 ]], outputs: [w31, w32]
     BLACKBOX::RANGE [w31]:1 bits []
     BLACKBOX::RANGE [w32]:32 bits []
-    EXPR [ (1, w21) (-4294967296, w31) (-1, w32) 4294967286 ]
-    EXPR [ (-1, w21, w31) (1, w21) (-1, w33) 0 ]
-    MEM (id: 0, read at: EXPR [ (1, w33) 0 ], value: EXPR [ (1, w34) 0 ]) 
-    EXPR [ (-1, w31, w34) (2, w31) (1, w34) (-1, w35) -2 ]
+    EXPR 1*w21 + -4294967296*w31 + -1*w32 + 4294967286 = 0
+    EXPR -1*w21*w31 + 1*w21 + -1*w33 + 0 = 0
+    MEM (id: 0, read at: EXPR [ (1, w33) 0 ], value: EXPR [ (1, w34) 0 ])
+    EXPR -1*w31*w34 + 2*w31 + 1*w34 + -1*w35 + -2 = 0
     BLACKBOX::RANGE [w35]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w36, w37]
     BLACKBOX::RANGE [w36]:1 bits []
     BLACKBOX::RANGE [w37]:32 bits []
-    EXPR [ (1, w21) (-4294967296, w36) (-1, w37) 4294967291 ]
-    EXPR [ (1, w31, w36) (-1, w36) 0 ]
-    EXPR [ (-1, w21, w31) (1, w21) (-1, w38) 0 ]
-    MEM (id: 0, read at: EXPR [ (1, w38) 0 ], value: EXPR [ (1, w39) 0 ]) 
-    MEM (id: 0, read at: EXPR [ (1, w27) 0 ], value: EXPR [ (1, w40) 0 ]) 
-    MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w41) 0 ]) 
-    EXPR [ (-1, w42) 2 ]
-    MEM (id: 0, read at: EXPR [ (1, w42) 0 ], value: EXPR [ (1, w43) 0 ]) 
-    EXPR [ (-1, w44) 3 ]
-    MEM (id: 0, read at: EXPR [ (1, w44) 0 ], value: EXPR [ (1, w45) 0 ]) 
-    EXPR [ (-1, w46) 4 ]
-    MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w47) 0 ]) 
+    EXPR 1*w21 + -4294967296*w36 + -1*w37 + 4294967291 = 0
+    EXPR 1*w31*w36 + -1*w36 + 0 = 0
+    EXPR -1*w21*w31 + 1*w21 + -1*w38 + 0 = 0
+    MEM (id: 0, read at: EXPR [ (1, w38) 0 ], value: EXPR [ (1, w39) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w27) 0 ], value: EXPR [ (1, w40) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w41) 0 ])
+    EXPR -1*w42 + 2 = 0
+    MEM (id: 0, read at: EXPR [ (1, w42) 0 ], value: EXPR [ (1, w43) 0 ])
+    EXPR -1*w44 + 3 = 0
+    MEM (id: 0, read at: EXPR [ (1, w44) 0 ], value: EXPR [ (1, w45) 0 ])
+    EXPR -1*w46 + 4 = 0
+    MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w47) 0 ])
     INIT (id: 3, len: 5, witnesses: [w40, w41, w43, w45, w47])
-    EXPR [ (-1, w31, w35) (1, w31, w39) (1, w35) (-1, w48) 0 ]
-    MEM (id: 3, write EXPR [ (1, w48) 0 ] at: EXPR [ (1, w38) 0 ]) 
-    MEM (id: 3, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w49) 0 ]) 
-    MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w50) 0 ]) 
-    EXPR [ (-1, w31, w36) 0 ]
-    EXPR [ (1, w21, w31) (-1, w51) 0 ]
-    MEM (id: 0, read at: EXPR [ (1, w51) 0 ], value: EXPR [ (1, w52) 0 ]) 
-    EXPR [ (-1, w31, w52) (1, w52) (-1, w53) 0 ]
-    MEM (id: 0, write EXPR [ (1, w53) 0 ] at: EXPR [ (1, w51) 0 ]) 
-    MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w54) 0 ]) 
-    EXPR [ (-1, w31) (-1, w55) 1 ]
-    EXPR [ (-1, w31, w49) (1, w31, w50) (1, w49) (-1, w56) 0 ]
-    EXPR [ (1, w31, w54) (1, w55, w56) -109 ]
-    EXPR [ (-1, w57) 246 ]
-    EXPR [ (-1, w58) 159 ]
-    EXPR [ (-1, w59) 32 ]
-    EXPR [ (-1, w60) 176 ]
-    EXPR [ (-1, w61) 8 ]
+    EXPR -1*w31*w35 + 1*w31*w39 + 1*w35 + -1*w48 + 0 = 0
+    MEM (id: 3, write EXPR [ (1, w48) 0 ] at: EXPR [ (1, w38) 0 ])
+    MEM (id: 3, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w49) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w50) 0 ])
+    EXPR -1*w31*w36 + 0 = 0
+    EXPR 1*w21*w31 + -1*w51 + 0 = 0
+    MEM (id: 0, read at: EXPR [ (1, w51) 0 ], value: EXPR [ (1, w52) 0 ])
+    EXPR -1*w31*w52 + 1*w52 + -1*w53 + 0 = 0
+    MEM (id: 0, write EXPR [ (1, w53) 0 ] at: EXPR [ (1, w51) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w54) 0 ])
+    EXPR -1*w31 + -1*w55 + 1 = 0
+    EXPR -1*w31*w49 + 1*w31*w50 + 1*w49 + -1*w56 + 0 = 0
+    EXPR 1*w31*w54 + 1*w55*w56 + -109 = 0
+    EXPR -1*w57 + 246 = 0
+    EXPR -1*w58 + 159 = 0
+    EXPR -1*w59 + 32 = 0
+    EXPR -1*w60 + 176 = 0
+    EXPR -1*w61 + 8 = 0
     INIT (id: 4, len: 5, witnesses: [w57, w58, w59, w60, w61])
-    MEM (id: 4, read at: EXPR [ (1, w7) 0 ], value: EXPR [ (1, w62) 0 ]) 
-    MEM (id: 4, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w63) 0 ]) 
-    MEM (id: 4, read at: EXPR [ (1, w9) 0 ], value: EXPR [ (1, w64) 0 ]) 
-    MEM (id: 4, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w65) 0 ]) 
-    MEM (id: 4, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w66) 0 ]) 
+    MEM (id: 4, read at: EXPR [ (1, w7) 0 ], value: EXPR [ (1, w62) 0 ])
+    MEM (id: 4, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w63) 0 ])
+    MEM (id: 4, read at: EXPR [ (1, w9) 0 ], value: EXPR [ (1, w64) 0 ])
+    MEM (id: 4, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w65) 0 ])
+    MEM (id: 4, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w66) 0 ])
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w62) (1, w63) (1, w64) (1, w65) (1, w66) 0 ]], outputs: [w67]
-    EXPR [ (1, w62, w67) (1, w63, w67) (1, w64, w67) (1, w65, w67) (1, w66, w67) -1 ]
+    EXPR 1*w62*w67 + 1*w63*w67 + 1*w64*w67 + 1*w65*w67 + 1*w66*w67 + -1 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w18) 0 ], EXPR [ 4294967296 ]], outputs: [w68, w69]
     BLACKBOX::RANGE [w68]:222 bits []
     BLACKBOX::RANGE [w69]:32 bits []
-    EXPR [ (1, w18) (-4294967296, w68) (-1, w69) 0 ]
-    EXPR [ (-1, w68) (-1, w70) 5096253676302562286669017222071363378443840053029366383258766538131 ]
+    EXPR 1*w18 + -4294967296*w68 + -1*w69 + 0 = 0
+    EXPR -1*w68 + -1*w70 + 5096253676302562286669017222071363378443840053029366383258766538131 = 0
     BLACKBOX::RANGE [w70]:222 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (-1, w68) 5096253676302562286669017222071363378443840053029366383258766538131 ]], outputs: [w71]
-    EXPR [ (-1, w68, w71) (5096253676302562286669017222071363378443840053029366383258766538131, w71) (1, w72) -1 ]
-    EXPR [ (-1, w68, w72) (5096253676302562286669017222071363378443840053029366383258766538131, w72) 0 ]
-    EXPR [ (1, w69, w72) (268435455, w72) (-1, w73) 0 ]
+    EXPR -1*w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + 1*w72 + -1 = 0
+    EXPR -1*w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72 + 0 = 0
+    EXPR 1*w69*w72 + 268435455*w72 + -1*w73 + 0 = 0
     BLACKBOX::RANGE [w73]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (-1, w69) 4294967299 ], EXPR [ 4294967296 ]], outputs: [w74, w75]
     BLACKBOX::RANGE [w74]:1 bits []
     BLACKBOX::RANGE [w75]:32 bits []
-    EXPR [ (-1, w69) (-4294967296, w74) (-1, w75) 4294967299 ]
-    EXPR [ (-1, w17, w74) (1, w17) (-3, w74) (-1, w76) 3 ]
+    EXPR -1*w69 + -4294967296*w74 + -1*w75 + 4294967299 = 0
+    EXPR -1*w17*w74 + 1*w17 + -3*w74 + -1*w76 + 3 = 0
     BLACKBOX::RANGE [w76]:32 bits []
-    EXPR [ (-1, w74, w76) (1, w76) (-1, w77) 0 ]
-    MEM (id: 1, read at: EXPR [ (1, w77) 0 ], value: EXPR [ (1, w78) 0 ]) 
-    EXPR [ (1, w15, w74) (-1, w74, w78) (-1, w15) (1, w78) 0 ]
+    EXPR -1*w74*w76 + 1*w76 + -1*w77 + 0 = 0
+    MEM (id: 1, read at: EXPR [ (1, w77) 0 ], value: EXPR [ (1, w78) 0 ])
+    EXPR 1*w15*w74 + -1*w74*w78 + -1*w15 + 1*w78 + 0 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -711,15 +711,15 @@ fn fold_basic() {
     return values: []
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w2]
-    
+
     func 1
     current witness: w3
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
-    EXPR [ (1, w0, w3) (-1, w1, w3) -1 ]
-    EXPR [ (-1, w0) (1, w2) 0 ]
+    EXPR 1*w0*w3 + -1*w1*w3 + -1 = 0
+    EXPR -1*w0 + 1*w2 + 0 = 0
     ";
     assert_program_roundtrip(src);
 }
@@ -734,7 +734,7 @@ fn fold_basic_mismatched_ids() {
     return values: []
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w2]
-    
+
     func 2
     current witness: w3
     private parameters: [w0, w1]
diff --git a/acvm-repo/acir/src/parser/token.rs b/acvm-repo/acir/src/parser/token.rs
index 8bd00af391f..b8fb6f4fd97 100644
--- a/acvm-repo/acir/src/parser/token.rs
+++ b/acvm-repo/acir/src/parser/token.rs
@@ -48,6 +48,12 @@ pub(crate) enum Token {
     LeftParen,
     /// )
     RightParen,
+    /// +
+    Plus,
+    /// *
+    Star,
+    /// =
+    Equal,
     Eof,
 }
 
@@ -75,6 +81,9 @@ impl std::fmt::Display for Token {
             Token::RightBracket => write!(f, "]"),
             Token::LeftParen => write!(f, "("),
             Token::RightParen => write!(f, ")"),
+            Token::Plus => write!(f, "+"),
+            Token::Star => write!(f, "*"),
+            Token::Equal => write!(f, "="),
             Token::Eof => write!(f, "(end of stream)"),
         }
     }
diff --git a/acvm-repo/acvm/src/compiler/optimizers/general.rs b/acvm-repo/acvm/src/compiler/optimizers/general.rs
index 41ccc1e6dec..fa7b98cdcb5 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/general.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/general.rs
@@ -102,7 +102,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR [ (1, w0, w1) 0 ]
+        EXPR 1*w0*w1 + 0 = 0
         ");
     }
 
@@ -124,7 +124,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR [ (1, w1) 0 ]
+        EXPR 1*w1 + 0 = 0
         ");
     }
 
@@ -147,7 +147,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR [ (9, w0, w1) 0 ]
+        EXPR 9*w0*w1 + 0 = 0
         ");
     }
 
@@ -167,7 +167,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR [ 0 ]
+        EXPR 0 = 0
         ");
     }
 
@@ -190,7 +190,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR [ (6, w0) 0 ]
+        EXPR 6*w0 + 0 = 0
         ");
     }
 
@@ -210,7 +210,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR [ 0 ]
+        EXPR 0 = 0
         ");
     }
 }
diff --git a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
index d574f8dd6d8..308c8e421aa 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
@@ -348,8 +348,8 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR [ (1, w0, w1) (1, w5) 0 ]
-        EXPR [ (2, w0, w0) (-1, w3) (2, w5) 0 ]
+        EXPR 1*w0*w1 + 1*w5 + 0 = 0
+        EXPR 2*w0*w0 + -1*w3 + 2*w5 + 0 = 0
         BLACKBOX::RANGE [w3]:32 bits []
         ");
     }
diff --git a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
index 38e743400a1..b1bb893065a 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
@@ -366,10 +366,10 @@ mod tests {
         public parameters: []
         return values: []
         BLACKBOX::RANGE [w1]:16 bits []
-        EXPR [ 0 ]
-        EXPR [ 0 ]
-        EXPR [ 0 ]
-        EXPR [ 0 ]
+        EXPR 0 = 0
+        EXPR 0 = 0
+        EXPR 0 = 0
+        EXPR 0 = 0
         ");
     }
 
@@ -395,7 +395,7 @@ mod tests {
         private parameters: []
         public parameters: []
         return values: []
-        EXPR [ (1, w1) 0 ]
+        EXPR 1*w1 + 0 = 0
         ");
     }
 
@@ -444,7 +444,7 @@ mod tests {
         BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: []
         BLACKBOX::RANGE [w1]:16 bits []
         BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: []
-        EXPR [ (1, w1) 0 ]
+        EXPR 1*w1 + 0 = 0
         ");
 
         // Applying again should have no effect (despite the range having the same bit size as the assert).
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index f45df4b61d8..1abcf3834d4 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -49,12 +49,12 @@ fn constant_array_access_out_of_bounds() {
     private parameters: []
     public parameters: []
     return values: []
-    EXPR [ (-1, w0) 0 ]
-    EXPR [ (-1, w1) 1 ]
+    EXPR -1*w0 + 0 = 0
+    EXPR -1*w1 + 1 = 0
     INIT (id: 0, len: 2, witnesses: [w0, w1])
-    EXPR [ (-1, w2) 5 ]
-    MEM (id: 0, read at: EXPR [ (1, w2) 0 ], value: EXPR [ (1, w3) 0 ]) 
-    EXPR [ (1, w3) 0 ]
+    EXPR -1*w2 + 5 = 0
+    MEM (id: 0, read at: EXPR [ (1, w2) 0 ], value: EXPR [ (1, w3) 0 ])
+    EXPR 1*w3 + 0 = 0
     ");
 }
 
@@ -96,8 +96,8 @@ fn generates_memory_op_for_dynamic_read() {
     public parameters: []
     return values: []
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
-    MEM (id: 0, read at: EXPR [ (1, w3) 0 ], value: EXPR [ (1, w4) 0 ]) 
-    EXPR [ (1, w4) -10 ]
+    MEM (id: 0, read at: EXPR [ (1, w3) 0 ], value: EXPR [ (1, w4) 0 ])
+    EXPR 1*w4 + -10 = 0
     ");
 }
 
@@ -120,17 +120,17 @@ fn generates_memory_op_for_dynamic_write() {
     public parameters: []
     return values: [w4, w5, w6]
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
-    EXPR [ (-1, w7) 10 ]
-    MEM (id: 1, write EXPR [ (1, w7) 0 ] at: EXPR [ (1, w3) 0 ]) 
-    EXPR [ (-1, w8) 0 ]
-    MEM (id: 1, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ]) 
-    EXPR [ (-1, w10) 1 ]
-    MEM (id: 1, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w11) 0 ]) 
-    EXPR [ (-1, w12) 2 ]
-    MEM (id: 1, read at: EXPR [ (1, w12) 0 ], value: EXPR [ (1, w13) 0 ]) 
-    EXPR [ (1, w4) (-1, w9) 0 ]
-    EXPR [ (1, w5) (-1, w11) 0 ]
-    EXPR [ (1, w6) (-1, w13) 0 ]
+    EXPR -1*w7 + 10 = 0
+    MEM (id: 1, write EXPR [ (1, w7) 0 ] at: EXPR [ (1, w3) 0 ])
+    EXPR -1*w8 + 0 = 0
+    MEM (id: 1, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ])
+    EXPR -1*w10 + 1 = 0
+    MEM (id: 1, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w11) 0 ])
+    EXPR -1*w12 + 2 = 0
+    MEM (id: 1, read at: EXPR [ (1, w12) 0 ], value: EXPR [ (1, w13) 0 ])
+    EXPR 1*w4 + -1*w9 + 0 = 0
+    EXPR 1*w5 + -1*w11 + 0 = 0
+    EXPR 1*w6 + -1*w13 + 0 = 0
     ");
 }
 
@@ -161,9 +161,9 @@ fn generates_predicated_index_for_dynamic_read() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR [ (1, w3, w4) (-1, w5) 0 ]
-    MEM (id: 0, read at: EXPR [ (1, w5) 0 ], value: EXPR [ (1, w6) 0 ]) 
-    EXPR [ (1, w6) -10 ]
+    EXPR 1*w3*w4 + -1*w5 + 0 = 0
+    MEM (id: 0, read at: EXPR [ (1, w5) 0 ], value: EXPR [ (1, w6) 0 ])
+    EXPR 1*w6 + -10 = 0
     ");
 }
 
@@ -199,20 +199,20 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR [ (1, w3, w4) (-1, w8) 0 ]
-    MEM (id: 0, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ]) 
+    EXPR 1*w3*w4 + -1*w8 + 0 = 0
+    MEM (id: 0, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ])
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
-    EXPR [ (-1, w4, w9) (10, w4) (1, w9) (-1, w10) 0 ]
-    MEM (id: 1, write EXPR [ (1, w10) 0 ] at: EXPR [ (1, w8) 0 ]) 
-    EXPR [ (-1, w11) 0 ]
-    MEM (id: 1, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w12) 0 ]) 
-    EXPR [ (-1, w13) 1 ]
-    MEM (id: 1, read at: EXPR [ (1, w13) 0 ], value: EXPR [ (1, w14) 0 ]) 
-    EXPR [ (-1, w15) 2 ]
-    MEM (id: 1, read at: EXPR [ (1, w15) 0 ], value: EXPR [ (1, w16) 0 ]) 
-    EXPR [ (1, w5) (-1, w12) 0 ]
-    EXPR [ (1, w6) (-1, w14) 0 ]
-    EXPR [ (1, w7) (-1, w16) 0 ]
+    EXPR -1*w4*w9 + 10*w4 + 1*w9 + -1*w10 + 0 = 0
+    MEM (id: 1, write EXPR [ (1, w10) 0 ] at: EXPR [ (1, w8) 0 ])
+    EXPR -1*w11 + 0 = 0
+    MEM (id: 1, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w12) 0 ])
+    EXPR -1*w13 + 1 = 0
+    MEM (id: 1, read at: EXPR [ (1, w13) 0 ], value: EXPR [ (1, w14) 0 ])
+    EXPR -1*w15 + 2 = 0
+    MEM (id: 1, read at: EXPR [ (1, w15) 0 ], value: EXPR [ (1, w16) 0 ])
+    EXPR 1*w5 + -1*w12 + 0 = 0
+    EXPR 1*w6 + -1*w14 + 0 = 0
+    EXPR 1*w7 + -1*w16 + 0 = 0
     ");
 }
 
@@ -237,7 +237,7 @@ fn zero_length_array_constant() {
     private parameters: []
     public parameters: []
     return values: []
-    EXPR [ 1 ]
+    EXPR 1 = 0
     ");
 }
 
@@ -264,6 +264,6 @@ fn zero_length_array_dynamic_predicate() {
     private parameters: [w0]
     public parameters: []
     return values: []
-    EXPR [ (1, w0) 0 ]
+    EXPR 1*w0 + 0 = 0
     ");
 }
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index e0cd71fc08c..dc7ce82389e 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -153,22 +153,22 @@ fn multiple_brillig_stdlib_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
-    EXPR [ (1, w1, w3) -1 ]
+    EXPR 1*w1*w3 + -1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR [ (1, w1) (-1, w5) (-1, w6) -1 ]
+    EXPR 1*w1 + -1*w5 + -1*w6 + -1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR [ (-1, w1, w4) (1, w0) (-1, w5) 0 ]
-    EXPR [ (-1, w2) (1, w4) 0 ]
+    EXPR -1*w1*w4 + 1*w0 + -1*w5 + 0 = 0
+    EXPR -1*w2 + 1*w4 + 0 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w7]
-    EXPR [ (1, w2, w7) -1 ]
+    EXPR 1*w2*w7 + -1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w8, w9]
     BLACKBOX::RANGE [w9]:32 bits []
-    EXPR [ (1, w2) (-1, w9) (-1, w10) -1 ]
+    EXPR 1*w2 + -1*w9 + -1*w10 + -1 = 0
     BLACKBOX::RANGE [w10]:32 bits []
-    EXPR [ (-1, w2, w8) (1, w1) (-1, w9) 0 ]
-    EXPR [ (1, w8) -1 ]
+    EXPR -1*w2*w8 + 1*w1 + -1*w9 + 0 = 0
+    EXPR 1*w8 + -1 = 0
 
     unconstrained func 0
     0: @21 = const u32 1
@@ -241,26 +241,26 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
-    EXPR [ (1, w1, w3) -1 ]
+    EXPR 1*w1*w3 + -1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR [ (1, w1) (-1, w5) (-1, w6) -1 ]
+    EXPR 1*w1 + -1*w5 + -1*w6 + -1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR [ (-1, w1, w4) (1, w0) (-1, w5) 0 ]
-    EXPR [ (-1, w2) (1, w4) 0 ]
+    EXPR -1*w1*w4 + 1*w0 + -1*w5 + 0 = 0
+    EXPR -1*w2 + 1*w4 + 0 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
     BLACKBOX::RANGE [w8]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w9]
-    EXPR [ (1, w2, w9) -1 ]
+    EXPR 1*w2*w9 + -1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w10, w11]
     BLACKBOX::RANGE [w11]:32 bits []
-    EXPR [ (1, w2) (-1, w11) (-1, w12) -1 ]
+    EXPR 1*w2 + -1*w11 + -1*w12 + -1 = 0
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR [ (-1, w2, w10) (1, w1) (-1, w11) 0 ]
-    EXPR [ (1, w10) -1 ]
+    EXPR -1*w2*w10 + 1*w1 + -1*w11 + 0 = 0
+    EXPR 1*w10 + -1 = 0
 
     unconstrained func 0
      0: @2 = const u32 1
@@ -375,14 +375,14 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
-    EXPR [ (1, w1, w3) -1 ]
+    EXPR 1*w1*w3 + -1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR [ (1, w1) (-1, w5) (-1, w6) -1 ]
+    EXPR 1*w1 + -1*w5 + -1*w6 + -1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR [ (-1, w1, w4) (1, w0) (-1, w5) 0 ]
-    EXPR [ (-1, w2) (1, w4) 0 ]
+    EXPR -1*w1*w4 + 1*w0 + -1*w5 + 0 = 0
+    EXPR -1*w2 + 1*w4 + 0 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
@@ -390,13 +390,13 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w9]
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w10]
-    EXPR [ (1, w2, w10) -1 ]
+    EXPR 1*w2*w10 + -1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w11, w12]
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR [ (1, w2) (-1, w12) (-1, w13) -1 ]
+    EXPR 1*w2 + -1*w12 + -1*w13 + -1 = 0
     BLACKBOX::RANGE [w13]:32 bits []
-    EXPR [ (-1, w2, w11) (1, w1) (-1, w12) 0 ]
-    EXPR [ (1, w11) -1 ]
+    EXPR -1*w2*w11 + 1*w1 + -1*w12 + 0 = 0
+    EXPR 1*w11 + -1 = 0
 
     func 1
     current witness: w5
@@ -405,12 +405,12 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR [ (1, w0) (-1, w1) (-1, w3) 0 ]
+    EXPR 1*w0 + -1*w1 + -1*w3 + 0 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w3) 0 ]], outputs: [w4]
-    EXPR [ (1, w3, w4) (1, w5) -1 ]
-    EXPR [ (1, w3, w5) 0 ]
-    EXPR [ (1, w5) 0 ]
-    EXPR [ (-1, w0) (1, w2) 0 ]
+    EXPR 1*w3*w4 + 1*w5 + -1 = 0
+    EXPR 1*w3*w5 + 0 = 0
+    EXPR 1*w5 + 0 = 0
+    EXPR -1*w0 + 1*w2 + 0 = 0
 
     unconstrained func 0
      0: @2 = const u32 1
diff --git a/compiler/noirc_evaluator/src/acir/tests/call.rs b/compiler/noirc_evaluator/src/acir/tests/call.rs
index 5424d82abb3..990bf406ee7 100644
--- a/compiler/noirc_evaluator/src/acir/tests/call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/call.rs
@@ -64,15 +64,15 @@ fn basic_call_with_outputs_assert(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR [ (1, w2) (-1, w3) 0 ]
-    
+    EXPR 1*w2 + -1*w3 + 0 = 0
+
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR [ (1, w0) (-1, w1) 0 ]
-    EXPR [ (-1, w0) (1, w2) 0 ]
+    EXPR 1*w0 + -1*w1 + 0 = 0
+    EXPR -1*w0 + 1*w2 + 0 = 0
     ");
 }
 
@@ -107,15 +107,15 @@ fn call_output_as_next_call_input(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w2, w1], outputs: [w3]
-    EXPR [ (1, w2) (-1, w3) 0 ]
-    
+    EXPR 1*w2 + -1*w3 + 0 = 0
+
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR [ (1, w0) (-1, w1) 0 ]
-    EXPR [ (-1, w0) (1, w2) 0 ]
+    EXPR 1*w0 + -1*w1 + 0 = 0
+    EXPR -1*w0 + 1*w2 + 0 = 0
     ");
 }
 
@@ -154,24 +154,24 @@ fn basic_nested_call(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR [ (1, w2) (-1, w3) 0 ]
-    
+    EXPR 1*w2 + -1*w3 + 0 = 0
+
     func 1
     current witness: w4
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR [ (1, w0) (-1, w3) 2 ]
+    EXPR 1*w0 + -1*w3 + 2 = 0
     CALL func 2: PREDICATE: EXPR [ 1 ]
     inputs: [w3, w1], outputs: [w4]
-    EXPR [ (1, w2) (-1, w4) 0 ]
-    
+    EXPR 1*w2 + -1*w4 + 0 = 0
+
     func 2
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR [ (1, w0) (-1, w1) 0 ]
-    EXPR [ (-1, w0) (1, w2) 0 ]
+    EXPR 1*w0 + -1*w1 + 0 = 0
+    EXPR -1*w0 + 1*w2 + 0 = 0
     ");
 }
diff --git a/compiler/noirc_evaluator/src/acir/tests/mod.rs b/compiler/noirc_evaluator/src/acir/tests/mod.rs
index 49620a12b2b..f47659e7104 100644
--- a/compiler/noirc_evaluator/src/acir/tests/mod.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/mod.rs
@@ -95,7 +95,7 @@ fn unchecked_mul_should_not_have_range_check() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR [ (-1, w0, w1) (1, w2) 0 ]
+    EXPR -1*w0*w1 + 1*w2 + 0 = 0
     ");
 }
 

From 6fb656bafb253ede3212c0056bbda3411c412b2a Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 12:11:04 -0300
Subject: [PATCH 02/25] Omit zero coefficients

---
 acvm-repo/acir/src/circuit/opcodes.rs         | 10 +-
 acvm-repo/acir/src/parser/mod.rs              |  5 +-
 acvm-repo/acir/src/parser/tests.rs            | 94 +++++++++----------
 .../acvm/src/compiler/optimizers/general.rs   |  8 +-
 .../compiler/optimizers/merge_expressions.rs  |  4 +-
 .../compiler/optimizers/redundant_range.rs    |  4 +-
 .../noirc_evaluator/src/acir/tests/arrays.rs  | 28 +++---
 .../src/acir/tests/brillig_call.rs            | 26 ++---
 .../noirc_evaluator/src/acir/tests/call.rs    | 20 ++--
 .../noirc_evaluator/src/acir/tests/mod.rs     |  2 +-
 10 files changed, 102 insertions(+), 99 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index 3a169e535f2..5e32fd26f8d 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -169,11 +169,15 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                     printed_term = true;
                 }
 
-                if printed_term {
-                    write!(f, " + ")?;
+                if !expr.q_c.is_zero()
+                    || (expr.mul_terms.is_empty() && expr.linear_combinations.is_empty())
+                {
+                    if printed_term {
+                        write!(f, " + ")?;
+                    }
+                    write!(f, "{}", expr.q_c)?;
                 }
 
-                write!(f, "{}", expr.q_c)?;
                 write!(f, " = 0")?;
 
                 Ok(())
diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index 2fe2deb6323..b348c923523 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -317,9 +317,8 @@ impl<'a> Parser<'a> {
             return Err(ParserError::ExpectedZero { found: zero_token, span });
         }
 
-        let Some(q_c) = constant else {
-            return Err(ParserError::MissingConstantTerm { span: self.token.span() });
-        };
+        // If a constant isn't provided, we default it to zero
+        let q_c = constant.unwrap_or_default();
 
         Ok(Expression { mul_terms, linear_combinations, q_c })
     }
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index f28a2a9eb85..8224a759c8c 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -102,11 +102,11 @@ fn assert_zero_opcodes() {
     private parameters: [w0, w1, w2, w3, w4]
     public parameters: [w5, w6, w7, w8, w9]
     return values: []
-    EXPR 1*w0 + -1*w5 + 0 = 0
-    EXPR 1*w1 + -1*w6 + 0 = 0
-    EXPR 1*w2 + -1*w7 + 0 = 0
-    EXPR 1*w3 + -1*w8 + 0 = 0
-    EXPR 1*w4 + -1*w9 + 0 = 0
+    EXPR 1*w0 + -1*w5 = 0
+    EXPR 1*w1 + -1*w6 = 0
+    EXPR 1*w2 + -1*w7 = 0
+    EXPR 1*w3 + -1*w8 = 0
+    EXPR 1*w4 + -1*w9 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -118,11 +118,11 @@ fn assert_zero_with_mul_terms() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    EXPR 1*w0*w1 + -1*w3 + 0 = 0
-    EXPR 1*w3*w3 + -1*w4 + 0 = 0
-    EXPR 1*w4*w4 + -1*w5 + 0 = 0
-    EXPR 1*w5*w5 + -1*w6 + 0 = 0
-    EXPR -1*w2 + 1*w6 + 0 = 0
+    EXPR 1*w0*w1 + -1*w3 = 0
+    EXPR 1*w3*w3 + -1*w4 = 0
+    EXPR 1*w4*w4 + -1*w5 = 0
+    EXPR 1*w5*w5 + -1*w6 = 0
+    EXPR -1*w2 + 1*w6 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -223,22 +223,22 @@ fn aes128_encrypt() {
     BLACKBOX::RANGE [w58]:8 bits []
     BLACKBOX::RANGE [w59]:8 bits []
     BLACKBOX::AES128_ENCRYPT [w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43] [w60, w61, w62, w63, w64, w65, w66, w67, w68, w69, w70, w71, w72, w73, w74, w75]
-    EXPR -1*w44 + 1*w60 + 0 = 0
-    EXPR -1*w45 + 1*w61 + 0 = 0
-    EXPR -1*w46 + 1*w62 + 0 = 0
-    EXPR -1*w47 + 1*w63 + 0 = 0
-    EXPR -1*w48 + 1*w64 + 0 = 0
-    EXPR -1*w49 + 1*w65 + 0 = 0
-    EXPR -1*w50 + 1*w66 + 0 = 0
-    EXPR -1*w51 + 1*w67 + 0 = 0
-    EXPR -1*w52 + 1*w68 + 0 = 0
-    EXPR -1*w53 + 1*w69 + 0 = 0
-    EXPR -1*w54 + 1*w70 + 0 = 0
-    EXPR -1*w55 + 1*w71 + 0 = 0
-    EXPR -1*w56 + 1*w72 + 0 = 0
-    EXPR -1*w57 + 1*w73 + 0 = 0
-    EXPR -1*w58 + 1*w74 + 0 = 0
-    EXPR -1*w59 + 1*w75 + 0 = 0
+    EXPR -1*w44 + 1*w60 = 0
+    EXPR -1*w45 + 1*w61 = 0
+    EXPR -1*w46 + 1*w62 = 0
+    EXPR -1*w47 + 1*w63 = 0
+    EXPR -1*w48 + 1*w64 = 0
+    EXPR -1*w49 + 1*w65 = 0
+    EXPR -1*w50 + 1*w66 = 0
+    EXPR -1*w51 + 1*w67 = 0
+    EXPR -1*w52 + 1*w68 = 0
+    EXPR -1*w53 + 1*w69 = 0
+    EXPR -1*w54 + 1*w70 = 0
+    EXPR -1*w55 + 1*w71 = 0
+    EXPR -1*w56 + 1*w72 = 0
+    EXPR -1*w57 + 1*w73 = 0
+    EXPR -1*w58 + 1*w74 = 0
+    EXPR -1*w59 + 1*w75 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -526,7 +526,7 @@ fn brillig_call() {
     return values: []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
     EXPR 1*w0*w3 + -1*w1*w3 + -1 = 0
-    EXPR -1*w0 + 1*w2 + 0 = 0
+    EXPR -1*w0 + 1*w2 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -541,7 +541,7 @@ fn brillig_call_with_predicate() {
     BRILLIG CALL func 0: PREDICATE: EXPR [ 1 ]
     inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
     EXPR 1*w0*w3 + -1*w1*w3 + -1 = 0
-    EXPR -1*w0 + 1*w2 + 0 = 0
+    EXPR -1*w0 + 1*w2 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -606,9 +606,9 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w15]:32 bits []
     BLACKBOX::RANGE [w16]:32 bits []
     BLACKBOX::RANGE [w17]:32 bits []
-    EXPR 5*w6 + -1*w19 + 0 = 0
+    EXPR 5*w6 + -1*w19 = 0
     BLACKBOX::RANGE [w19]:32 bits []
-    EXPR 1*w5 + -1*w19 + -1*w20 + 0 = 0
+    EXPR 1*w5 + -1*w19 + -1*w20 = 0
     BLACKBOX::RANGE [w20]:32 bits []
     EXPR 1*w20 + -1*w21 + -5 = 0
     EXPR 1*w21 + -1*w22 + -3 = 0
@@ -619,19 +619,19 @@ fn array_dynamic() {
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w22) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w25, w26]
     BLACKBOX::RANGE [w26]:32 bits []
     EXPR 1*w22 + -4294967296*w25 + -1*w26 + 4294967291 = 0
-    EXPR -1*w25 + 0 = 0
-    EXPR -1*w27 + 0 = 0
+    EXPR -1*w25 = 0
+    EXPR -1*w27 = 0
     MEM (id: 0, write EXPR [ (1, w27) 0 ] at: EXPR [ (1, w22) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w28) 0 ])
     EXPR 1*w28 + -111 = 0
     EXPR -1*w29 + 1 = 0
     MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w30) 0 ])
-    EXPR 1*w30 + 0 = 0
+    EXPR 1*w30 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967286 ], EXPR [ 4294967296 ]], outputs: [w31, w32]
     BLACKBOX::RANGE [w31]:1 bits []
     BLACKBOX::RANGE [w32]:32 bits []
     EXPR 1*w21 + -4294967296*w31 + -1*w32 + 4294967286 = 0
-    EXPR -1*w21*w31 + 1*w21 + -1*w33 + 0 = 0
+    EXPR -1*w21*w31 + 1*w21 + -1*w33 = 0
     MEM (id: 0, read at: EXPR [ (1, w33) 0 ], value: EXPR [ (1, w34) 0 ])
     EXPR -1*w31*w34 + 2*w31 + 1*w34 + -1*w35 + -2 = 0
     BLACKBOX::RANGE [w35]:32 bits []
@@ -639,8 +639,8 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w36]:1 bits []
     BLACKBOX::RANGE [w37]:32 bits []
     EXPR 1*w21 + -4294967296*w36 + -1*w37 + 4294967291 = 0
-    EXPR 1*w31*w36 + -1*w36 + 0 = 0
-    EXPR -1*w21*w31 + 1*w21 + -1*w38 + 0 = 0
+    EXPR 1*w31*w36 + -1*w36 = 0
+    EXPR -1*w21*w31 + 1*w21 + -1*w38 = 0
     MEM (id: 0, read at: EXPR [ (1, w38) 0 ], value: EXPR [ (1, w39) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w27) 0 ], value: EXPR [ (1, w40) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w41) 0 ])
@@ -651,18 +651,18 @@ fn array_dynamic() {
     EXPR -1*w46 + 4 = 0
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w47) 0 ])
     INIT (id: 3, len: 5, witnesses: [w40, w41, w43, w45, w47])
-    EXPR -1*w31*w35 + 1*w31*w39 + 1*w35 + -1*w48 + 0 = 0
+    EXPR -1*w31*w35 + 1*w31*w39 + 1*w35 + -1*w48 = 0
     MEM (id: 3, write EXPR [ (1, w48) 0 ] at: EXPR [ (1, w38) 0 ])
     MEM (id: 3, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w49) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w50) 0 ])
-    EXPR -1*w31*w36 + 0 = 0
-    EXPR 1*w21*w31 + -1*w51 + 0 = 0
+    EXPR -1*w31*w36 = 0
+    EXPR 1*w21*w31 + -1*w51 = 0
     MEM (id: 0, read at: EXPR [ (1, w51) 0 ], value: EXPR [ (1, w52) 0 ])
-    EXPR -1*w31*w52 + 1*w52 + -1*w53 + 0 = 0
+    EXPR -1*w31*w52 + 1*w52 + -1*w53 = 0
     MEM (id: 0, write EXPR [ (1, w53) 0 ] at: EXPR [ (1, w51) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w54) 0 ])
     EXPR -1*w31 + -1*w55 + 1 = 0
-    EXPR -1*w31*w49 + 1*w31*w50 + 1*w49 + -1*w56 + 0 = 0
+    EXPR -1*w31*w49 + 1*w31*w50 + 1*w49 + -1*w56 = 0
     EXPR 1*w31*w54 + 1*w55*w56 + -109 = 0
     EXPR -1*w57 + 246 = 0
     EXPR -1*w58 + 159 = 0
@@ -680,13 +680,13 @@ fn array_dynamic() {
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w18) 0 ], EXPR [ 4294967296 ]], outputs: [w68, w69]
     BLACKBOX::RANGE [w68]:222 bits []
     BLACKBOX::RANGE [w69]:32 bits []
-    EXPR 1*w18 + -4294967296*w68 + -1*w69 + 0 = 0
+    EXPR 1*w18 + -4294967296*w68 + -1*w69 = 0
     EXPR -1*w68 + -1*w70 + 5096253676302562286669017222071363378443840053029366383258766538131 = 0
     BLACKBOX::RANGE [w70]:222 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (-1, w68) 5096253676302562286669017222071363378443840053029366383258766538131 ]], outputs: [w71]
     EXPR -1*w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + 1*w72 + -1 = 0
-    EXPR -1*w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72 + 0 = 0
-    EXPR 1*w69*w72 + 268435455*w72 + -1*w73 + 0 = 0
+    EXPR -1*w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72 = 0
+    EXPR 1*w69*w72 + 268435455*w72 + -1*w73 = 0
     BLACKBOX::RANGE [w73]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (-1, w69) 4294967299 ], EXPR [ 4294967296 ]], outputs: [w74, w75]
     BLACKBOX::RANGE [w74]:1 bits []
@@ -694,9 +694,9 @@ fn array_dynamic() {
     EXPR -1*w69 + -4294967296*w74 + -1*w75 + 4294967299 = 0
     EXPR -1*w17*w74 + 1*w17 + -3*w74 + -1*w76 + 3 = 0
     BLACKBOX::RANGE [w76]:32 bits []
-    EXPR -1*w74*w76 + 1*w76 + -1*w77 + 0 = 0
+    EXPR -1*w74*w76 + 1*w76 + -1*w77 = 0
     MEM (id: 1, read at: EXPR [ (1, w77) 0 ], value: EXPR [ (1, w78) 0 ])
-    EXPR 1*w15*w74 + -1*w74*w78 + -1*w15 + 1*w78 + 0 = 0
+    EXPR 1*w15*w74 + -1*w74*w78 + -1*w15 + 1*w78 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -719,7 +719,7 @@ fn fold_basic() {
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
     EXPR 1*w0*w3 + -1*w1*w3 + -1 = 0
-    EXPR -1*w0 + 1*w2 + 0 = 0
+    EXPR -1*w0 + 1*w2 = 0
     ";
     assert_program_roundtrip(src);
 }
diff --git a/acvm-repo/acvm/src/compiler/optimizers/general.rs b/acvm-repo/acvm/src/compiler/optimizers/general.rs
index fa7b98cdcb5..e9fcb6a23a6 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/general.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/general.rs
@@ -102,7 +102,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 1*w0*w1 + 0 = 0
+        EXPR 1*w0*w1 = 0
         ");
     }
 
@@ -124,7 +124,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 1*w1 + 0 = 0
+        EXPR 1*w1 = 0
         ");
     }
 
@@ -147,7 +147,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 9*w0*w1 + 0 = 0
+        EXPR 9*w0*w1 = 0
         ");
     }
 
@@ -190,7 +190,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 6*w0 + 0 = 0
+        EXPR 6*w0 = 0
         ");
     }
 
diff --git a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
index 308c8e421aa..7e746068dc7 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
@@ -348,8 +348,8 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 1*w0*w1 + 1*w5 + 0 = 0
-        EXPR 2*w0*w0 + -1*w3 + 2*w5 + 0 = 0
+        EXPR 1*w0*w1 + 1*w5 = 0
+        EXPR 2*w0*w0 + -1*w3 + 2*w5 = 0
         BLACKBOX::RANGE [w3]:32 bits []
         ");
     }
diff --git a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
index b1bb893065a..25ea648dae1 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
@@ -395,7 +395,7 @@ mod tests {
         private parameters: []
         public parameters: []
         return values: []
-        EXPR 1*w1 + 0 = 0
+        EXPR 1*w1 = 0
         ");
     }
 
@@ -444,7 +444,7 @@ mod tests {
         BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: []
         BLACKBOX::RANGE [w1]:16 bits []
         BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: []
-        EXPR 1*w1 + 0 = 0
+        EXPR 1*w1 = 0
         ");
 
         // Applying again should have no effect (despite the range having the same bit size as the assert).
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index 1abcf3834d4..ebf12c54811 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -49,12 +49,12 @@ fn constant_array_access_out_of_bounds() {
     private parameters: []
     public parameters: []
     return values: []
-    EXPR -1*w0 + 0 = 0
+    EXPR -1*w0 = 0
     EXPR -1*w1 + 1 = 0
     INIT (id: 0, len: 2, witnesses: [w0, w1])
     EXPR -1*w2 + 5 = 0
     MEM (id: 0, read at: EXPR [ (1, w2) 0 ], value: EXPR [ (1, w3) 0 ])
-    EXPR 1*w3 + 0 = 0
+    EXPR 1*w3 = 0
     ");
 }
 
@@ -122,15 +122,15 @@ fn generates_memory_op_for_dynamic_write() {
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
     EXPR -1*w7 + 10 = 0
     MEM (id: 1, write EXPR [ (1, w7) 0 ] at: EXPR [ (1, w3) 0 ])
-    EXPR -1*w8 + 0 = 0
+    EXPR -1*w8 = 0
     MEM (id: 1, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ])
     EXPR -1*w10 + 1 = 0
     MEM (id: 1, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w11) 0 ])
     EXPR -1*w12 + 2 = 0
     MEM (id: 1, read at: EXPR [ (1, w12) 0 ], value: EXPR [ (1, w13) 0 ])
-    EXPR 1*w4 + -1*w9 + 0 = 0
-    EXPR 1*w5 + -1*w11 + 0 = 0
-    EXPR 1*w6 + -1*w13 + 0 = 0
+    EXPR 1*w4 + -1*w9 = 0
+    EXPR 1*w5 + -1*w11 = 0
+    EXPR 1*w6 + -1*w13 = 0
     ");
 }
 
@@ -161,7 +161,7 @@ fn generates_predicated_index_for_dynamic_read() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR 1*w3*w4 + -1*w5 + 0 = 0
+    EXPR 1*w3*w4 + -1*w5 = 0
     MEM (id: 0, read at: EXPR [ (1, w5) 0 ], value: EXPR [ (1, w6) 0 ])
     EXPR 1*w6 + -10 = 0
     ");
@@ -199,20 +199,20 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR 1*w3*w4 + -1*w8 + 0 = 0
+    EXPR 1*w3*w4 + -1*w8 = 0
     MEM (id: 0, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ])
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
-    EXPR -1*w4*w9 + 10*w4 + 1*w9 + -1*w10 + 0 = 0
+    EXPR -1*w4*w9 + 10*w4 + 1*w9 + -1*w10 = 0
     MEM (id: 1, write EXPR [ (1, w10) 0 ] at: EXPR [ (1, w8) 0 ])
-    EXPR -1*w11 + 0 = 0
+    EXPR -1*w11 = 0
     MEM (id: 1, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w12) 0 ])
     EXPR -1*w13 + 1 = 0
     MEM (id: 1, read at: EXPR [ (1, w13) 0 ], value: EXPR [ (1, w14) 0 ])
     EXPR -1*w15 + 2 = 0
     MEM (id: 1, read at: EXPR [ (1, w15) 0 ], value: EXPR [ (1, w16) 0 ])
-    EXPR 1*w5 + -1*w12 + 0 = 0
-    EXPR 1*w6 + -1*w14 + 0 = 0
-    EXPR 1*w7 + -1*w16 + 0 = 0
+    EXPR 1*w5 + -1*w12 = 0
+    EXPR 1*w6 + -1*w14 = 0
+    EXPR 1*w7 + -1*w16 = 0
     ");
 }
 
@@ -264,6 +264,6 @@ fn zero_length_array_dynamic_predicate() {
     private parameters: [w0]
     public parameters: []
     return values: []
-    EXPR 1*w0 + 0 = 0
+    EXPR 1*w0 = 0
     ");
 }
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index dc7ce82389e..b4d5edc1955 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -159,15 +159,15 @@ fn multiple_brillig_stdlib_calls() {
     BLACKBOX::RANGE [w5]:32 bits []
     EXPR 1*w1 + -1*w5 + -1*w6 + -1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + 1*w0 + -1*w5 + 0 = 0
-    EXPR -1*w2 + 1*w4 + 0 = 0
+    EXPR -1*w1*w4 + 1*w0 + -1*w5 = 0
+    EXPR -1*w2 + 1*w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w7]
     EXPR 1*w2*w7 + -1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w8, w9]
     BLACKBOX::RANGE [w9]:32 bits []
     EXPR 1*w2 + -1*w9 + -1*w10 + -1 = 0
     BLACKBOX::RANGE [w10]:32 bits []
-    EXPR -1*w2*w8 + 1*w1 + -1*w9 + 0 = 0
+    EXPR -1*w2*w8 + 1*w1 + -1*w9 = 0
     EXPR 1*w8 + -1 = 0
 
     unconstrained func 0
@@ -247,8 +247,8 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BLACKBOX::RANGE [w5]:32 bits []
     EXPR 1*w1 + -1*w5 + -1*w6 + -1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + 1*w0 + -1*w5 + 0 = 0
-    EXPR -1*w2 + 1*w4 + 0 = 0
+    EXPR -1*w1*w4 + 1*w0 + -1*w5 = 0
+    EXPR -1*w2 + 1*w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
@@ -259,7 +259,7 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BLACKBOX::RANGE [w11]:32 bits []
     EXPR 1*w2 + -1*w11 + -1*w12 + -1 = 0
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR -1*w2*w10 + 1*w1 + -1*w11 + 0 = 0
+    EXPR -1*w2*w10 + 1*w1 + -1*w11 = 0
     EXPR 1*w10 + -1 = 0
 
     unconstrained func 0
@@ -381,8 +381,8 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w5]:32 bits []
     EXPR 1*w1 + -1*w5 + -1*w6 + -1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + 1*w0 + -1*w5 + 0 = 0
-    EXPR -1*w2 + 1*w4 + 0 = 0
+    EXPR -1*w1*w4 + 1*w0 + -1*w5 = 0
+    EXPR -1*w2 + 1*w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
@@ -395,7 +395,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w12]:32 bits []
     EXPR 1*w2 + -1*w12 + -1*w13 + -1 = 0
     BLACKBOX::RANGE [w13]:32 bits []
-    EXPR -1*w2*w11 + 1*w1 + -1*w12 + 0 = 0
+    EXPR -1*w2*w11 + 1*w1 + -1*w12 = 0
     EXPR 1*w11 + -1 = 0
 
     func 1
@@ -405,12 +405,12 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR 1*w0 + -1*w1 + -1*w3 + 0 = 0
+    EXPR 1*w0 + -1*w1 + -1*w3 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w3) 0 ]], outputs: [w4]
     EXPR 1*w3*w4 + 1*w5 + -1 = 0
-    EXPR 1*w3*w5 + 0 = 0
-    EXPR 1*w5 + 0 = 0
-    EXPR -1*w0 + 1*w2 + 0 = 0
+    EXPR 1*w3*w5 = 0
+    EXPR 1*w5 = 0
+    EXPR -1*w0 + 1*w2 = 0
 
     unconstrained func 0
      0: @2 = const u32 1
diff --git a/compiler/noirc_evaluator/src/acir/tests/call.rs b/compiler/noirc_evaluator/src/acir/tests/call.rs
index 990bf406ee7..4a2e469ab0d 100644
--- a/compiler/noirc_evaluator/src/acir/tests/call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/call.rs
@@ -64,15 +64,15 @@ fn basic_call_with_outputs_assert(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR 1*w2 + -1*w3 + 0 = 0
+    EXPR 1*w2 + -1*w3 = 0
 
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR 1*w0 + -1*w1 + 0 = 0
-    EXPR -1*w0 + 1*w2 + 0 = 0
+    EXPR 1*w0 + -1*w1 = 0
+    EXPR -1*w0 + 1*w2 = 0
     ");
 }
 
@@ -107,15 +107,15 @@ fn call_output_as_next_call_input(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w2, w1], outputs: [w3]
-    EXPR 1*w2 + -1*w3 + 0 = 0
+    EXPR 1*w2 + -1*w3 = 0
 
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR 1*w0 + -1*w1 + 0 = 0
-    EXPR -1*w0 + 1*w2 + 0 = 0
+    EXPR 1*w0 + -1*w1 = 0
+    EXPR -1*w0 + 1*w2 = 0
     ");
 }
 
@@ -154,7 +154,7 @@ fn basic_nested_call(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR 1*w2 + -1*w3 + 0 = 0
+    EXPR 1*w2 + -1*w3 = 0
 
     func 1
     current witness: w4
@@ -164,14 +164,14 @@ fn basic_nested_call(inline_type: InlineType) {
     EXPR 1*w0 + -1*w3 + 2 = 0
     CALL func 2: PREDICATE: EXPR [ 1 ]
     inputs: [w3, w1], outputs: [w4]
-    EXPR 1*w2 + -1*w4 + 0 = 0
+    EXPR 1*w2 + -1*w4 = 0
 
     func 2
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR 1*w0 + -1*w1 + 0 = 0
-    EXPR -1*w0 + 1*w2 + 0 = 0
+    EXPR 1*w0 + -1*w1 = 0
+    EXPR -1*w0 + 1*w2 = 0
     ");
 }
diff --git a/compiler/noirc_evaluator/src/acir/tests/mod.rs b/compiler/noirc_evaluator/src/acir/tests/mod.rs
index f47659e7104..c62dca3f6fa 100644
--- a/compiler/noirc_evaluator/src/acir/tests/mod.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/mod.rs
@@ -95,7 +95,7 @@ fn unchecked_mul_should_not_have_range_check() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR -1*w0*w1 + 1*w2 + 0 = 0
+    EXPR -1*w0*w1 + 1*w2 = 0
     ");
 }
 

From 88c085921ac25eaaf48ba85cdcc18118c649a31f Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 12:19:51 -0300
Subject: [PATCH 03/25] Don't write coefficient 1

---
 acvm-repo/acir/src/circuit/opcodes.rs         |  14 ++-
 acvm-repo/acir/src/parser/mod.rs              |  36 +++---
 acvm-repo/acir/src/parser/tests.rs            | 118 +++++++++---------
 .../acvm/src/compiler/optimizers/general.rs   |   4 +-
 .../compiler/optimizers/merge_expressions.rs  |   2 +-
 .../compiler/optimizers/redundant_range.rs    |   4 +-
 .../noirc_evaluator/src/acir/tests/arrays.rs  |  26 ++--
 .../src/acir/tests/brillig_call.rs            |  58 ++++-----
 .../noirc_evaluator/src/acir/tests/call.rs    |  22 ++--
 .../noirc_evaluator/src/acir/tests/mod.rs     |   2 +-
 10 files changed, 152 insertions(+), 134 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index 5e32fd26f8d..f589d664f56 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -156,7 +156,12 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                         write!(f, " + ")?;
                     }
 
-                    write!(f, "{coefficient}*{witness1}*{witness2}")?;
+                    if coefficient.is_one() {
+                        write!(f, "{witness1}*{witness2}")?;
+                    } else {
+                        write!(f, "{coefficient}*{witness1}*{witness2}")?;
+                    }
+
                     printed_term = true;
                 }
 
@@ -165,7 +170,12 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                         write!(f, " + ")?;
                     }
 
-                    write!(f, "{coefficient}*{witness}")?;
+                    if coefficient.is_one() {
+                        write!(f, "{witness}")?;
+                    } else {
+                        write!(f, "{coefficient}*{witness}")?;
+                    }
+
                     printed_term = true;
                 }
 
diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index b348c923523..89ee512a5ec 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -273,27 +273,35 @@ impl<'a> Parser<'a> {
         let mut constant: Option<FieldElement> = None;
 
         loop {
-            let Some(coefficient) = self.eat_field_element()? else {
-                return self.expected_field_element();
-            };
-
-            if self.eat(Token::Star)? {
-                let w1 = self.eat_witness_or_error()?;
-
+            if let Some(w1) = self.eat_witness()? {
+                let coefficient = FieldElement::one();
                 if self.eat(Token::Star)? {
                     let w2 = self.eat_witness_or_error()?;
                     mul_terms.push((coefficient, w1, w2));
                 } else {
                     linear_combinations.push((coefficient, w1));
                 }
-            } else {
-                if constant.is_some() {
-                    return Err(ParserError::DuplicatedConstantTerm {
-                        found: self.token.token().clone(),
-                        span: self.token.span(),
-                    });
+            } else if let Some(coefficient) = self.eat_field_element()? {
+                if self.eat(Token::Star)? {
+                    let w1 = self.eat_witness_or_error()?;
+
+                    if self.eat(Token::Star)? {
+                        let w2 = self.eat_witness_or_error()?;
+                        mul_terms.push((coefficient, w1, w2));
+                    } else {
+                        linear_combinations.push((coefficient, w1));
+                    }
+                } else {
+                    if constant.is_some() {
+                        return Err(ParserError::DuplicatedConstantTerm {
+                            found: self.token.token().clone(),
+                            span: self.token.span(),
+                        });
+                    }
+                    constant = Some(coefficient);
                 }
-                constant = Some(coefficient);
+            } else {
+                return self.expected_field_element();
             }
 
             if self.eat(Token::Plus)? {
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 8224a759c8c..2b2d615257c 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -102,11 +102,11 @@ fn assert_zero_opcodes() {
     private parameters: [w0, w1, w2, w3, w4]
     public parameters: [w5, w6, w7, w8, w9]
     return values: []
-    EXPR 1*w0 + -1*w5 = 0
-    EXPR 1*w1 + -1*w6 = 0
-    EXPR 1*w2 + -1*w7 = 0
-    EXPR 1*w3 + -1*w8 = 0
-    EXPR 1*w4 + -1*w9 = 0
+    EXPR w0 + -1*w5 = 0
+    EXPR w1 + -1*w6 = 0
+    EXPR w2 + -1*w7 = 0
+    EXPR w3 + -1*w8 = 0
+    EXPR w4 + -1*w9 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -118,11 +118,11 @@ fn assert_zero_with_mul_terms() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    EXPR 1*w0*w1 + -1*w3 = 0
-    EXPR 1*w3*w3 + -1*w4 = 0
-    EXPR 1*w4*w4 + -1*w5 = 0
-    EXPR 1*w5*w5 + -1*w6 = 0
-    EXPR -1*w2 + 1*w6 = 0
+    EXPR w0*w1 + -1*w3 = 0
+    EXPR w3*w3 + -1*w4 = 0
+    EXPR w4*w4 + -1*w5 = 0
+    EXPR w5*w5 + -1*w6 = 0
+    EXPR -1*w2 + w6 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -149,7 +149,7 @@ fn xor() {
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::XOR [w0, w1]:32 bits [w2]
-    EXPR 1*w2 + -15 = 0
+    EXPR w2 + -15 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -223,22 +223,22 @@ fn aes128_encrypt() {
     BLACKBOX::RANGE [w58]:8 bits []
     BLACKBOX::RANGE [w59]:8 bits []
     BLACKBOX::AES128_ENCRYPT [w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43] [w60, w61, w62, w63, w64, w65, w66, w67, w68, w69, w70, w71, w72, w73, w74, w75]
-    EXPR -1*w44 + 1*w60 = 0
-    EXPR -1*w45 + 1*w61 = 0
-    EXPR -1*w46 + 1*w62 = 0
-    EXPR -1*w47 + 1*w63 = 0
-    EXPR -1*w48 + 1*w64 = 0
-    EXPR -1*w49 + 1*w65 = 0
-    EXPR -1*w50 + 1*w66 = 0
-    EXPR -1*w51 + 1*w67 = 0
-    EXPR -1*w52 + 1*w68 = 0
-    EXPR -1*w53 + 1*w69 = 0
-    EXPR -1*w54 + 1*w70 = 0
-    EXPR -1*w55 + 1*w71 = 0
-    EXPR -1*w56 + 1*w72 = 0
-    EXPR -1*w57 + 1*w73 = 0
-    EXPR -1*w58 + 1*w74 = 0
-    EXPR -1*w59 + 1*w75 = 0
+    EXPR -1*w44 + w60 = 0
+    EXPR -1*w45 + w61 = 0
+    EXPR -1*w46 + w62 = 0
+    EXPR -1*w47 + w63 = 0
+    EXPR -1*w48 + w64 = 0
+    EXPR -1*w49 + w65 = 0
+    EXPR -1*w50 + w66 = 0
+    EXPR -1*w51 + w67 = 0
+    EXPR -1*w52 + w68 = 0
+    EXPR -1*w53 + w69 = 0
+    EXPR -1*w54 + w70 = 0
+    EXPR -1*w55 + w71 = 0
+    EXPR -1*w56 + w72 = 0
+    EXPR -1*w57 + w73 = 0
+    EXPR -1*w58 + w74 = 0
+    EXPR -1*w59 + w75 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -525,8 +525,8 @@ fn brillig_call() {
     public parameters: []
     return values: []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
-    EXPR 1*w0*w3 + -1*w1*w3 + -1 = 0
-    EXPR -1*w0 + 1*w2 = 0
+    EXPR w0*w3 + -1*w1*w3 + -1 = 0
+    EXPR -1*w0 + w2 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -540,8 +540,8 @@ fn brillig_call_with_predicate() {
     return values: []
     BRILLIG CALL func 0: PREDICATE: EXPR [ 1 ]
     inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
-    EXPR 1*w0*w3 + -1*w1*w3 + -1 = 0
-    EXPR -1*w0 + 1*w2 = 0
+    EXPR w0*w3 + -1*w1*w3 + -1 = 0
+    EXPR -1*w0 + w2 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -608,39 +608,39 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w17]:32 bits []
     EXPR 5*w6 + -1*w19 = 0
     BLACKBOX::RANGE [w19]:32 bits []
-    EXPR 1*w5 + -1*w19 + -1*w20 = 0
+    EXPR w5 + -1*w19 + -1*w20 = 0
     BLACKBOX::RANGE [w20]:32 bits []
-    EXPR 1*w20 + -1*w21 + -5 = 0
-    EXPR 1*w21 + -1*w22 + -3 = 0
+    EXPR w20 + -1*w21 + -5 = 0
+    EXPR w21 + -1*w22 + -3 = 0
     MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w23) 0 ])
-    EXPR 1*w23 + -111 = 0
+    EXPR w23 + -111 = 0
     MEM (id: 0, read at: EXPR [ (1, w22) 0 ], value: EXPR [ (1, w24) 0 ])
-    EXPR 1*w24 + -101 = 0
+    EXPR w24 + -101 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w22) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w25, w26]
     BLACKBOX::RANGE [w26]:32 bits []
-    EXPR 1*w22 + -4294967296*w25 + -1*w26 + 4294967291 = 0
+    EXPR w22 + -4294967296*w25 + -1*w26 + 4294967291 = 0
     EXPR -1*w25 = 0
     EXPR -1*w27 = 0
     MEM (id: 0, write EXPR [ (1, w27) 0 ] at: EXPR [ (1, w22) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w28) 0 ])
-    EXPR 1*w28 + -111 = 0
+    EXPR w28 + -111 = 0
     EXPR -1*w29 + 1 = 0
     MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w30) 0 ])
-    EXPR 1*w30 = 0
+    EXPR w30 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967286 ], EXPR [ 4294967296 ]], outputs: [w31, w32]
     BLACKBOX::RANGE [w31]:1 bits []
     BLACKBOX::RANGE [w32]:32 bits []
-    EXPR 1*w21 + -4294967296*w31 + -1*w32 + 4294967286 = 0
-    EXPR -1*w21*w31 + 1*w21 + -1*w33 = 0
+    EXPR w21 + -4294967296*w31 + -1*w32 + 4294967286 = 0
+    EXPR -1*w21*w31 + w21 + -1*w33 = 0
     MEM (id: 0, read at: EXPR [ (1, w33) 0 ], value: EXPR [ (1, w34) 0 ])
-    EXPR -1*w31*w34 + 2*w31 + 1*w34 + -1*w35 + -2 = 0
+    EXPR -1*w31*w34 + 2*w31 + w34 + -1*w35 + -2 = 0
     BLACKBOX::RANGE [w35]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w36, w37]
     BLACKBOX::RANGE [w36]:1 bits []
     BLACKBOX::RANGE [w37]:32 bits []
-    EXPR 1*w21 + -4294967296*w36 + -1*w37 + 4294967291 = 0
-    EXPR 1*w31*w36 + -1*w36 = 0
-    EXPR -1*w21*w31 + 1*w21 + -1*w38 = 0
+    EXPR w21 + -4294967296*w36 + -1*w37 + 4294967291 = 0
+    EXPR w31*w36 + -1*w36 = 0
+    EXPR -1*w21*w31 + w21 + -1*w38 = 0
     MEM (id: 0, read at: EXPR [ (1, w38) 0 ], value: EXPR [ (1, w39) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w27) 0 ], value: EXPR [ (1, w40) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w41) 0 ])
@@ -651,19 +651,19 @@ fn array_dynamic() {
     EXPR -1*w46 + 4 = 0
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w47) 0 ])
     INIT (id: 3, len: 5, witnesses: [w40, w41, w43, w45, w47])
-    EXPR -1*w31*w35 + 1*w31*w39 + 1*w35 + -1*w48 = 0
+    EXPR -1*w31*w35 + w31*w39 + w35 + -1*w48 = 0
     MEM (id: 3, write EXPR [ (1, w48) 0 ] at: EXPR [ (1, w38) 0 ])
     MEM (id: 3, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w49) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w50) 0 ])
     EXPR -1*w31*w36 = 0
-    EXPR 1*w21*w31 + -1*w51 = 0
+    EXPR w21*w31 + -1*w51 = 0
     MEM (id: 0, read at: EXPR [ (1, w51) 0 ], value: EXPR [ (1, w52) 0 ])
-    EXPR -1*w31*w52 + 1*w52 + -1*w53 = 0
+    EXPR -1*w31*w52 + w52 + -1*w53 = 0
     MEM (id: 0, write EXPR [ (1, w53) 0 ] at: EXPR [ (1, w51) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w54) 0 ])
     EXPR -1*w31 + -1*w55 + 1 = 0
-    EXPR -1*w31*w49 + 1*w31*w50 + 1*w49 + -1*w56 = 0
-    EXPR 1*w31*w54 + 1*w55*w56 + -109 = 0
+    EXPR -1*w31*w49 + w31*w50 + w49 + -1*w56 = 0
+    EXPR w31*w54 + w55*w56 + -109 = 0
     EXPR -1*w57 + 246 = 0
     EXPR -1*w58 + 159 = 0
     EXPR -1*w59 + 32 = 0
@@ -676,27 +676,27 @@ fn array_dynamic() {
     MEM (id: 4, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w65) 0 ])
     MEM (id: 4, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w66) 0 ])
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w62) (1, w63) (1, w64) (1, w65) (1, w66) 0 ]], outputs: [w67]
-    EXPR 1*w62*w67 + 1*w63*w67 + 1*w64*w67 + 1*w65*w67 + 1*w66*w67 + -1 = 0
+    EXPR w62*w67 + w63*w67 + w64*w67 + w65*w67 + w66*w67 + -1 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w18) 0 ], EXPR [ 4294967296 ]], outputs: [w68, w69]
     BLACKBOX::RANGE [w68]:222 bits []
     BLACKBOX::RANGE [w69]:32 bits []
-    EXPR 1*w18 + -4294967296*w68 + -1*w69 = 0
+    EXPR w18 + -4294967296*w68 + -1*w69 = 0
     EXPR -1*w68 + -1*w70 + 5096253676302562286669017222071363378443840053029366383258766538131 = 0
     BLACKBOX::RANGE [w70]:222 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (-1, w68) 5096253676302562286669017222071363378443840053029366383258766538131 ]], outputs: [w71]
-    EXPR -1*w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + 1*w72 + -1 = 0
+    EXPR -1*w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + w72 + -1 = 0
     EXPR -1*w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72 = 0
-    EXPR 1*w69*w72 + 268435455*w72 + -1*w73 = 0
+    EXPR w69*w72 + 268435455*w72 + -1*w73 = 0
     BLACKBOX::RANGE [w73]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (-1, w69) 4294967299 ], EXPR [ 4294967296 ]], outputs: [w74, w75]
     BLACKBOX::RANGE [w74]:1 bits []
     BLACKBOX::RANGE [w75]:32 bits []
     EXPR -1*w69 + -4294967296*w74 + -1*w75 + 4294967299 = 0
-    EXPR -1*w17*w74 + 1*w17 + -3*w74 + -1*w76 + 3 = 0
+    EXPR -1*w17*w74 + w17 + -3*w74 + -1*w76 + 3 = 0
     BLACKBOX::RANGE [w76]:32 bits []
-    EXPR -1*w74*w76 + 1*w76 + -1*w77 = 0
+    EXPR -1*w74*w76 + w76 + -1*w77 = 0
     MEM (id: 1, read at: EXPR [ (1, w77) 0 ], value: EXPR [ (1, w78) 0 ])
-    EXPR 1*w15*w74 + -1*w74*w78 + -1*w15 + 1*w78 = 0
+    EXPR w15*w74 + -1*w74*w78 + -1*w15 + w78 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -718,8 +718,8 @@ fn fold_basic() {
     public parameters: []
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
-    EXPR 1*w0*w3 + -1*w1*w3 + -1 = 0
-    EXPR -1*w0 + 1*w2 = 0
+    EXPR w0*w3 + -1*w1*w3 + -1 = 0
+    EXPR -1*w0 + w2 = 0
     ";
     assert_program_roundtrip(src);
 }
diff --git a/acvm-repo/acvm/src/compiler/optimizers/general.rs b/acvm-repo/acvm/src/compiler/optimizers/general.rs
index e9fcb6a23a6..e28f7bf95d1 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/general.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/general.rs
@@ -102,7 +102,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 1*w0*w1 = 0
+        EXPR w0*w1 = 0
         ");
     }
 
@@ -124,7 +124,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 1*w1 = 0
+        EXPR w1 = 0
         ");
     }
 
diff --git a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
index 7e746068dc7..668f222187e 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
@@ -348,7 +348,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 1*w0*w1 + 1*w5 = 0
+        EXPR w0*w1 + w5 = 0
         EXPR 2*w0*w0 + -1*w3 + 2*w5 = 0
         BLACKBOX::RANGE [w3]:32 bits []
         ");
diff --git a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
index 25ea648dae1..131f6445de3 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
@@ -395,7 +395,7 @@ mod tests {
         private parameters: []
         public parameters: []
         return values: []
-        EXPR 1*w1 = 0
+        EXPR w1 = 0
         ");
     }
 
@@ -444,7 +444,7 @@ mod tests {
         BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: []
         BLACKBOX::RANGE [w1]:16 bits []
         BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: []
-        EXPR 1*w1 = 0
+        EXPR w1 = 0
         ");
 
         // Applying again should have no effect (despite the range having the same bit size as the assert).
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index ebf12c54811..76205aa8be6 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -54,7 +54,7 @@ fn constant_array_access_out_of_bounds() {
     INIT (id: 0, len: 2, witnesses: [w0, w1])
     EXPR -1*w2 + 5 = 0
     MEM (id: 0, read at: EXPR [ (1, w2) 0 ], value: EXPR [ (1, w3) 0 ])
-    EXPR 1*w3 = 0
+    EXPR w3 = 0
     ");
 }
 
@@ -97,7 +97,7 @@ fn generates_memory_op_for_dynamic_read() {
     return values: []
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     MEM (id: 0, read at: EXPR [ (1, w3) 0 ], value: EXPR [ (1, w4) 0 ])
-    EXPR 1*w4 + -10 = 0
+    EXPR w4 + -10 = 0
     ");
 }
 
@@ -128,9 +128,9 @@ fn generates_memory_op_for_dynamic_write() {
     MEM (id: 1, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w11) 0 ])
     EXPR -1*w12 + 2 = 0
     MEM (id: 1, read at: EXPR [ (1, w12) 0 ], value: EXPR [ (1, w13) 0 ])
-    EXPR 1*w4 + -1*w9 = 0
-    EXPR 1*w5 + -1*w11 = 0
-    EXPR 1*w6 + -1*w13 = 0
+    EXPR w4 + -1*w9 = 0
+    EXPR w5 + -1*w11 = 0
+    EXPR w6 + -1*w13 = 0
     ");
 }
 
@@ -161,9 +161,9 @@ fn generates_predicated_index_for_dynamic_read() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR 1*w3*w4 + -1*w5 = 0
+    EXPR w3*w4 + -1*w5 = 0
     MEM (id: 0, read at: EXPR [ (1, w5) 0 ], value: EXPR [ (1, w6) 0 ])
-    EXPR 1*w6 + -10 = 0
+    EXPR w6 + -10 = 0
     ");
 }
 
@@ -199,10 +199,10 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR 1*w3*w4 + -1*w8 = 0
+    EXPR w3*w4 + -1*w8 = 0
     MEM (id: 0, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ])
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
-    EXPR -1*w4*w9 + 10*w4 + 1*w9 + -1*w10 = 0
+    EXPR -1*w4*w9 + 10*w4 + w9 + -1*w10 = 0
     MEM (id: 1, write EXPR [ (1, w10) 0 ] at: EXPR [ (1, w8) 0 ])
     EXPR -1*w11 = 0
     MEM (id: 1, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w12) 0 ])
@@ -210,9 +210,9 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     MEM (id: 1, read at: EXPR [ (1, w13) 0 ], value: EXPR [ (1, w14) 0 ])
     EXPR -1*w15 + 2 = 0
     MEM (id: 1, read at: EXPR [ (1, w15) 0 ], value: EXPR [ (1, w16) 0 ])
-    EXPR 1*w5 + -1*w12 = 0
-    EXPR 1*w6 + -1*w14 = 0
-    EXPR 1*w7 + -1*w16 = 0
+    EXPR w5 + -1*w12 = 0
+    EXPR w6 + -1*w14 = 0
+    EXPR w7 + -1*w16 = 0
     ");
 }
 
@@ -264,6 +264,6 @@ fn zero_length_array_dynamic_predicate() {
     private parameters: [w0]
     public parameters: []
     return values: []
-    EXPR 1*w0 = 0
+    EXPR w0 = 0
     ");
 }
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index b4d5edc1955..b231e6ea74d 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -153,22 +153,22 @@ fn multiple_brillig_stdlib_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
-    EXPR 1*w1*w3 + -1 = 0
+    EXPR w1*w3 + -1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR 1*w1 + -1*w5 + -1*w6 + -1 = 0
+    EXPR w1 + -1*w5 + -1*w6 + -1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + 1*w0 + -1*w5 = 0
-    EXPR -1*w2 + 1*w4 = 0
+    EXPR -1*w1*w4 + w0 + -1*w5 = 0
+    EXPR -1*w2 + w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w7]
-    EXPR 1*w2*w7 + -1 = 0
+    EXPR w2*w7 + -1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w8, w9]
     BLACKBOX::RANGE [w9]:32 bits []
-    EXPR 1*w2 + -1*w9 + -1*w10 + -1 = 0
+    EXPR w2 + -1*w9 + -1*w10 + -1 = 0
     BLACKBOX::RANGE [w10]:32 bits []
-    EXPR -1*w2*w8 + 1*w1 + -1*w9 = 0
-    EXPR 1*w8 + -1 = 0
+    EXPR -1*w2*w8 + w1 + -1*w9 = 0
+    EXPR w8 + -1 = 0
 
     unconstrained func 0
     0: @21 = const u32 1
@@ -241,26 +241,26 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
-    EXPR 1*w1*w3 + -1 = 0
+    EXPR w1*w3 + -1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR 1*w1 + -1*w5 + -1*w6 + -1 = 0
+    EXPR w1 + -1*w5 + -1*w6 + -1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + 1*w0 + -1*w5 = 0
-    EXPR -1*w2 + 1*w4 = 0
+    EXPR -1*w1*w4 + w0 + -1*w5 = 0
+    EXPR -1*w2 + w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
     BLACKBOX::RANGE [w8]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w9]
-    EXPR 1*w2*w9 + -1 = 0
+    EXPR w2*w9 + -1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w10, w11]
     BLACKBOX::RANGE [w11]:32 bits []
-    EXPR 1*w2 + -1*w11 + -1*w12 + -1 = 0
+    EXPR w2 + -1*w11 + -1*w12 + -1 = 0
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR -1*w2*w10 + 1*w1 + -1*w11 = 0
-    EXPR 1*w10 + -1 = 0
+    EXPR -1*w2*w10 + w1 + -1*w11 = 0
+    EXPR w10 + -1 = 0
 
     unconstrained func 0
      0: @2 = const u32 1
@@ -375,14 +375,14 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
-    EXPR 1*w1*w3 + -1 = 0
+    EXPR w1*w3 + -1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR 1*w1 + -1*w5 + -1*w6 + -1 = 0
+    EXPR w1 + -1*w5 + -1*w6 + -1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + 1*w0 + -1*w5 = 0
-    EXPR -1*w2 + 1*w4 = 0
+    EXPR -1*w1*w4 + w0 + -1*w5 = 0
+    EXPR -1*w2 + w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
@@ -390,13 +390,13 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w9]
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w10]
-    EXPR 1*w2*w10 + -1 = 0
+    EXPR w2*w10 + -1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w11, w12]
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR 1*w2 + -1*w12 + -1*w13 + -1 = 0
+    EXPR w2 + -1*w12 + -1*w13 + -1 = 0
     BLACKBOX::RANGE [w13]:32 bits []
-    EXPR -1*w2*w11 + 1*w1 + -1*w12 = 0
-    EXPR 1*w11 + -1 = 0
+    EXPR -1*w2*w11 + w1 + -1*w12 = 0
+    EXPR w11 + -1 = 0
 
     func 1
     current witness: w5
@@ -405,12 +405,12 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR 1*w0 + -1*w1 + -1*w3 = 0
+    EXPR w0 + -1*w1 + -1*w3 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w3) 0 ]], outputs: [w4]
-    EXPR 1*w3*w4 + 1*w5 + -1 = 0
-    EXPR 1*w3*w5 = 0
-    EXPR 1*w5 = 0
-    EXPR -1*w0 + 1*w2 = 0
+    EXPR w3*w4 + w5 + -1 = 0
+    EXPR w3*w5 = 0
+    EXPR w5 = 0
+    EXPR -1*w0 + w2 = 0
 
     unconstrained func 0
      0: @2 = const u32 1
diff --git a/compiler/noirc_evaluator/src/acir/tests/call.rs b/compiler/noirc_evaluator/src/acir/tests/call.rs
index 4a2e469ab0d..5884e36785a 100644
--- a/compiler/noirc_evaluator/src/acir/tests/call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/call.rs
@@ -64,15 +64,15 @@ fn basic_call_with_outputs_assert(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR 1*w2 + -1*w3 = 0
+    EXPR w2 + -1*w3 = 0
 
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR 1*w0 + -1*w1 = 0
-    EXPR -1*w0 + 1*w2 = 0
+    EXPR w0 + -1*w1 = 0
+    EXPR -1*w0 + w2 = 0
     ");
 }
 
@@ -107,15 +107,15 @@ fn call_output_as_next_call_input(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w2, w1], outputs: [w3]
-    EXPR 1*w2 + -1*w3 = 0
+    EXPR w2 + -1*w3 = 0
 
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR 1*w0 + -1*w1 = 0
-    EXPR -1*w0 + 1*w2 = 0
+    EXPR w0 + -1*w1 = 0
+    EXPR -1*w0 + w2 = 0
     ");
 }
 
@@ -154,24 +154,24 @@ fn basic_nested_call(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR 1*w2 + -1*w3 = 0
+    EXPR w2 + -1*w3 = 0
 
     func 1
     current witness: w4
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR 1*w0 + -1*w3 + 2 = 0
+    EXPR w0 + -1*w3 + 2 = 0
     CALL func 2: PREDICATE: EXPR [ 1 ]
     inputs: [w3, w1], outputs: [w4]
-    EXPR 1*w2 + -1*w4 = 0
+    EXPR w2 + -1*w4 = 0
 
     func 2
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR 1*w0 + -1*w1 = 0
-    EXPR -1*w0 + 1*w2 = 0
+    EXPR w0 + -1*w1 = 0
+    EXPR -1*w0 + w2 = 0
     ");
 }
diff --git a/compiler/noirc_evaluator/src/acir/tests/mod.rs b/compiler/noirc_evaluator/src/acir/tests/mod.rs
index c62dca3f6fa..088b42b246e 100644
--- a/compiler/noirc_evaluator/src/acir/tests/mod.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/mod.rs
@@ -95,7 +95,7 @@ fn unchecked_mul_should_not_have_range_check() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR -1*w0*w1 + 1*w2 = 0
+    EXPR -1*w0*w1 + w2 = 0
     ");
 }
 

From f78b8a9d2c4a989a9297d3ab9266bcacf2001582 Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 12:32:33 -0300
Subject: [PATCH 04/25] Use standalone minus when possible

---
 acvm-repo/acir/src/circuit/opcodes.rs         | 48 ++++++++++-
 acvm-repo/acir/src/parser/lexer.rs            |  3 +
 acvm-repo/acir/src/parser/mod.rs              | 11 +++
 acvm-repo/acir/src/parser/tests.rs            | 84 +++++++++----------
 acvm-repo/acir/src/parser/token.rs            |  3 +
 .../compiler/optimizers/merge_expressions.rs  |  2 +-
 .../noirc_evaluator/src/acir/tests/arrays.rs  | 22 ++---
 .../src/acir/tests/brillig_call.rs            | 46 +++++-----
 .../noirc_evaluator/src/acir/tests/call.rs    | 16 ++--
 9 files changed, 146 insertions(+), 89 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index f589d664f56..b1c200aa384 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -152,10 +152,23 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                 let mut printed_term = false;
 
                 for (coefficient, witness1, witness2) in &expr.mul_terms {
+                    let coefficient_as_string = coefficient.to_string();
+                    let coefficient_is_negative = coefficient_as_string.starts_with('-');
+
                     if printed_term {
-                        write!(f, " + ")?;
+                        if coefficient_is_negative {
+                            write!(f, " - ")?;
+                        } else {
+                            write!(f, " + ")?;
+                        }
                     }
 
+                    let coefficient = if printed_term && coefficient_is_negative {
+                        -*coefficient
+                    } else {
+                        *coefficient
+                    };
+
                     if coefficient.is_one() {
                         write!(f, "{witness1}*{witness2}")?;
                     } else {
@@ -166,10 +179,23 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                 }
 
                 for (coefficient, witness) in &expr.linear_combinations {
+                    let coefficient_as_string = coefficient.to_string();
+                    let coefficient_is_negative = coefficient_as_string.starts_with('-');
+
                     if printed_term {
-                        write!(f, " + ")?;
+                        if coefficient_is_negative {
+                            write!(f, " - ")?;
+                        } else {
+                            write!(f, " + ")?;
+                        }
                     }
 
+                    let coefficient = if printed_term && coefficient_is_negative {
+                        -*coefficient
+                    } else {
+                        *coefficient
+                    };
+
                     if coefficient.is_one() {
                         write!(f, "{witness}")?;
                     } else {
@@ -182,10 +208,24 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                 if !expr.q_c.is_zero()
                     || (expr.mul_terms.is_empty() && expr.linear_combinations.is_empty())
                 {
+                    let coefficient = expr.q_c;
+                    let coefficient_as_string = coefficient.to_string();
+                    let coefficient_is_negative = coefficient_as_string.starts_with('-');
+
                     if printed_term {
-                        write!(f, " + ")?;
+                        if coefficient_is_negative {
+                            write!(f, " - ")?;
+                        } else {
+                            write!(f, " + ")?;
+                        }
                     }
-                    write!(f, "{}", expr.q_c)?;
+
+                    let coefficient = if printed_term && coefficient_is_negative {
+                        -coefficient
+                    } else {
+                        coefficient
+                    };
+                    write!(f, "{coefficient}")?;
                 }
 
                 write!(f, " = 0")?;
diff --git a/acvm-repo/acir/src/parser/lexer.rs b/acvm-repo/acir/src/parser/lexer.rs
index c30b5badbd7..3c6d6592e8a 100644
--- a/acvm-repo/acir/src/parser/lexer.rs
+++ b/acvm-repo/acir/src/parser/lexer.rs
@@ -65,6 +65,9 @@ impl<'a> Lexer<'a> {
             ':' => self.single_char_token(Token::Colon),
             ';' => self.single_char_token(Token::Semicolon),
             '+' => self.single_char_token(Token::Plus),
+            '-' if self.peek_char().is_none_or(|char| !char.is_ascii_digit()) => {
+                self.single_char_token(Token::Minus)
+            }
             '*' => self.single_char_token(Token::Star),
             '=' => self.single_char_token(Token::Equal),
             'w' if self.peek_char().is_some_and(|char| char.is_ascii_digit()) => {
diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index 89ee512a5ec..61aea113f73 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -271,10 +271,13 @@ impl<'a> Parser<'a> {
         let mut linear_combinations = Vec::new();
         let mut mul_terms = Vec::new();
         let mut constant: Option<FieldElement> = None;
+        let mut negative = false;
 
         loop {
             if let Some(w1) = self.eat_witness()? {
                 let coefficient = FieldElement::one();
+                let coefficient = if negative { -coefficient } else { coefficient };
+
                 if self.eat(Token::Star)? {
                     let w2 = self.eat_witness_or_error()?;
                     mul_terms.push((coefficient, w1, w2));
@@ -282,6 +285,8 @@ impl<'a> Parser<'a> {
                     linear_combinations.push((coefficient, w1));
                 }
             } else if let Some(coefficient) = self.eat_field_element()? {
+                let coefficient = if negative { -coefficient } else { coefficient };
+
                 if self.eat(Token::Star)? {
                     let w1 = self.eat_witness_or_error()?;
 
@@ -305,6 +310,12 @@ impl<'a> Parser<'a> {
             }
 
             if self.eat(Token::Plus)? {
+                negative = false;
+                continue;
+            }
+
+            if self.eat(Token::Minus)? {
+                negative = true;
                 continue;
             }
 
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 2b2d615257c..353d3e794af 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -102,11 +102,11 @@ fn assert_zero_opcodes() {
     private parameters: [w0, w1, w2, w3, w4]
     public parameters: [w5, w6, w7, w8, w9]
     return values: []
-    EXPR w0 + -1*w5 = 0
-    EXPR w1 + -1*w6 = 0
-    EXPR w2 + -1*w7 = 0
-    EXPR w3 + -1*w8 = 0
-    EXPR w4 + -1*w9 = 0
+    EXPR w0 - w5 = 0
+    EXPR w1 - w6 = 0
+    EXPR w2 - w7 = 0
+    EXPR w3 - w8 = 0
+    EXPR w4 - w9 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -118,10 +118,10 @@ fn assert_zero_with_mul_terms() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    EXPR w0*w1 + -1*w3 = 0
-    EXPR w3*w3 + -1*w4 = 0
-    EXPR w4*w4 + -1*w5 = 0
-    EXPR w5*w5 + -1*w6 = 0
+    EXPR w0*w1 - w3 = 0
+    EXPR w3*w3 - w4 = 0
+    EXPR w4*w4 - w5 = 0
+    EXPR w5*w5 - w6 = 0
     EXPR -1*w2 + w6 = 0
     ";
     assert_circuit_roundtrip(src);
@@ -149,7 +149,7 @@ fn xor() {
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::XOR [w0, w1]:32 bits [w2]
-    EXPR w2 + -15 = 0
+    EXPR w2 - 15 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -525,7 +525,7 @@ fn brillig_call() {
     public parameters: []
     return values: []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
-    EXPR w0*w3 + -1*w1*w3 + -1 = 0
+    EXPR w0*w3 - w1*w3 - 1 = 0
     EXPR -1*w0 + w2 = 0
     ";
     assert_circuit_roundtrip(src);
@@ -540,7 +540,7 @@ fn brillig_call_with_predicate() {
     return values: []
     BRILLIG CALL func 0: PREDICATE: EXPR [ 1 ]
     inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
-    EXPR w0*w3 + -1*w1*w3 + -1 = 0
+    EXPR w0*w3 - w1*w3 - 1 = 0
     EXPR -1*w0 + w2 = 0
     ";
     assert_circuit_roundtrip(src);
@@ -606,41 +606,41 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w15]:32 bits []
     BLACKBOX::RANGE [w16]:32 bits []
     BLACKBOX::RANGE [w17]:32 bits []
-    EXPR 5*w6 + -1*w19 = 0
+    EXPR 5*w6 - w19 = 0
     BLACKBOX::RANGE [w19]:32 bits []
-    EXPR w5 + -1*w19 + -1*w20 = 0
+    EXPR w5 - w19 - w20 = 0
     BLACKBOX::RANGE [w20]:32 bits []
-    EXPR w20 + -1*w21 + -5 = 0
-    EXPR w21 + -1*w22 + -3 = 0
+    EXPR w20 - w21 - 5 = 0
+    EXPR w21 - w22 - 3 = 0
     MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w23) 0 ])
-    EXPR w23 + -111 = 0
+    EXPR w23 - 111 = 0
     MEM (id: 0, read at: EXPR [ (1, w22) 0 ], value: EXPR [ (1, w24) 0 ])
-    EXPR w24 + -101 = 0
+    EXPR w24 - 101 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w22) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w25, w26]
     BLACKBOX::RANGE [w26]:32 bits []
-    EXPR w22 + -4294967296*w25 + -1*w26 + 4294967291 = 0
+    EXPR w22 - 4294967296*w25 - w26 + 4294967291 = 0
     EXPR -1*w25 = 0
     EXPR -1*w27 = 0
     MEM (id: 0, write EXPR [ (1, w27) 0 ] at: EXPR [ (1, w22) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w28) 0 ])
-    EXPR w28 + -111 = 0
+    EXPR w28 - 111 = 0
     EXPR -1*w29 + 1 = 0
     MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w30) 0 ])
     EXPR w30 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967286 ], EXPR [ 4294967296 ]], outputs: [w31, w32]
     BLACKBOX::RANGE [w31]:1 bits []
     BLACKBOX::RANGE [w32]:32 bits []
-    EXPR w21 + -4294967296*w31 + -1*w32 + 4294967286 = 0
-    EXPR -1*w21*w31 + w21 + -1*w33 = 0
+    EXPR w21 - 4294967296*w31 - w32 + 4294967286 = 0
+    EXPR -1*w21*w31 + w21 - w33 = 0
     MEM (id: 0, read at: EXPR [ (1, w33) 0 ], value: EXPR [ (1, w34) 0 ])
-    EXPR -1*w31*w34 + 2*w31 + w34 + -1*w35 + -2 = 0
+    EXPR -1*w31*w34 + 2*w31 + w34 - w35 - 2 = 0
     BLACKBOX::RANGE [w35]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w36, w37]
     BLACKBOX::RANGE [w36]:1 bits []
     BLACKBOX::RANGE [w37]:32 bits []
-    EXPR w21 + -4294967296*w36 + -1*w37 + 4294967291 = 0
-    EXPR w31*w36 + -1*w36 = 0
-    EXPR -1*w21*w31 + w21 + -1*w38 = 0
+    EXPR w21 - 4294967296*w36 - w37 + 4294967291 = 0
+    EXPR w31*w36 - w36 = 0
+    EXPR -1*w21*w31 + w21 - w38 = 0
     MEM (id: 0, read at: EXPR [ (1, w38) 0 ], value: EXPR [ (1, w39) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w27) 0 ], value: EXPR [ (1, w40) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w41) 0 ])
@@ -651,19 +651,19 @@ fn array_dynamic() {
     EXPR -1*w46 + 4 = 0
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w47) 0 ])
     INIT (id: 3, len: 5, witnesses: [w40, w41, w43, w45, w47])
-    EXPR -1*w31*w35 + w31*w39 + w35 + -1*w48 = 0
+    EXPR -1*w31*w35 + w31*w39 + w35 - w48 = 0
     MEM (id: 3, write EXPR [ (1, w48) 0 ] at: EXPR [ (1, w38) 0 ])
     MEM (id: 3, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w49) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w50) 0 ])
     EXPR -1*w31*w36 = 0
-    EXPR w21*w31 + -1*w51 = 0
+    EXPR w21*w31 - w51 = 0
     MEM (id: 0, read at: EXPR [ (1, w51) 0 ], value: EXPR [ (1, w52) 0 ])
-    EXPR -1*w31*w52 + w52 + -1*w53 = 0
+    EXPR -1*w31*w52 + w52 - w53 = 0
     MEM (id: 0, write EXPR [ (1, w53) 0 ] at: EXPR [ (1, w51) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w54) 0 ])
-    EXPR -1*w31 + -1*w55 + 1 = 0
-    EXPR -1*w31*w49 + w31*w50 + w49 + -1*w56 = 0
-    EXPR w31*w54 + w55*w56 + -109 = 0
+    EXPR -1*w31 - w55 + 1 = 0
+    EXPR -1*w31*w49 + w31*w50 + w49 - w56 = 0
+    EXPR w31*w54 + w55*w56 - 109 = 0
     EXPR -1*w57 + 246 = 0
     EXPR -1*w58 + 159 = 0
     EXPR -1*w59 + 32 = 0
@@ -676,27 +676,27 @@ fn array_dynamic() {
     MEM (id: 4, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w65) 0 ])
     MEM (id: 4, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w66) 0 ])
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w62) (1, w63) (1, w64) (1, w65) (1, w66) 0 ]], outputs: [w67]
-    EXPR w62*w67 + w63*w67 + w64*w67 + w65*w67 + w66*w67 + -1 = 0
+    EXPR w62*w67 + w63*w67 + w64*w67 + w65*w67 + w66*w67 - 1 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w18) 0 ], EXPR [ 4294967296 ]], outputs: [w68, w69]
     BLACKBOX::RANGE [w68]:222 bits []
     BLACKBOX::RANGE [w69]:32 bits []
-    EXPR w18 + -4294967296*w68 + -1*w69 = 0
-    EXPR -1*w68 + -1*w70 + 5096253676302562286669017222071363378443840053029366383258766538131 = 0
+    EXPR w18 - 4294967296*w68 - w69 = 0
+    EXPR -1*w68 - w70 + 5096253676302562286669017222071363378443840053029366383258766538131 = 0
     BLACKBOX::RANGE [w70]:222 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (-1, w68) 5096253676302562286669017222071363378443840053029366383258766538131 ]], outputs: [w71]
-    EXPR -1*w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + w72 + -1 = 0
+    EXPR -1*w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + w72 - 1 = 0
     EXPR -1*w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72 = 0
-    EXPR w69*w72 + 268435455*w72 + -1*w73 = 0
+    EXPR w69*w72 + 268435455*w72 - w73 = 0
     BLACKBOX::RANGE [w73]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (-1, w69) 4294967299 ], EXPR [ 4294967296 ]], outputs: [w74, w75]
     BLACKBOX::RANGE [w74]:1 bits []
     BLACKBOX::RANGE [w75]:32 bits []
-    EXPR -1*w69 + -4294967296*w74 + -1*w75 + 4294967299 = 0
-    EXPR -1*w17*w74 + w17 + -3*w74 + -1*w76 + 3 = 0
+    EXPR -1*w69 - 4294967296*w74 - w75 + 4294967299 = 0
+    EXPR -1*w17*w74 + w17 - 3*w74 - w76 + 3 = 0
     BLACKBOX::RANGE [w76]:32 bits []
-    EXPR -1*w74*w76 + w76 + -1*w77 = 0
+    EXPR -1*w74*w76 + w76 - w77 = 0
     MEM (id: 1, read at: EXPR [ (1, w77) 0 ], value: EXPR [ (1, w78) 0 ])
-    EXPR w15*w74 + -1*w74*w78 + -1*w15 + w78 = 0
+    EXPR w15*w74 - w74*w78 - w15 + w78 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -718,7 +718,7 @@ fn fold_basic() {
     public parameters: []
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
-    EXPR w0*w3 + -1*w1*w3 + -1 = 0
+    EXPR w0*w3 - w1*w3 - 1 = 0
     EXPR -1*w0 + w2 = 0
     ";
     assert_program_roundtrip(src);
diff --git a/acvm-repo/acir/src/parser/token.rs b/acvm-repo/acir/src/parser/token.rs
index b8fb6f4fd97..7cc805ac06c 100644
--- a/acvm-repo/acir/src/parser/token.rs
+++ b/acvm-repo/acir/src/parser/token.rs
@@ -50,6 +50,8 @@ pub(crate) enum Token {
     RightParen,
     /// +
     Plus,
+    /// -
+    Minus,
     /// *
     Star,
     /// =
@@ -82,6 +84,7 @@ impl std::fmt::Display for Token {
             Token::LeftParen => write!(f, "("),
             Token::RightParen => write!(f, ")"),
             Token::Plus => write!(f, "+"),
+            Token::Minus => write!(f, "-"),
             Token::Star => write!(f, "*"),
             Token::Equal => write!(f, "="),
             Token::Eof => write!(f, "(end of stream)"),
diff --git a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
index 668f222187e..9d1d9134cd7 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
@@ -349,7 +349,7 @@ mod tests {
         public parameters: []
         return values: []
         EXPR w0*w1 + w5 = 0
-        EXPR 2*w0*w0 + -1*w3 + 2*w5 = 0
+        EXPR 2*w0*w0 - w3 + 2*w5 = 0
         BLACKBOX::RANGE [w3]:32 bits []
         ");
     }
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index 76205aa8be6..0f7f54b63a3 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -97,7 +97,7 @@ fn generates_memory_op_for_dynamic_read() {
     return values: []
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     MEM (id: 0, read at: EXPR [ (1, w3) 0 ], value: EXPR [ (1, w4) 0 ])
-    EXPR w4 + -10 = 0
+    EXPR w4 - 10 = 0
     ");
 }
 
@@ -128,9 +128,9 @@ fn generates_memory_op_for_dynamic_write() {
     MEM (id: 1, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w11) 0 ])
     EXPR -1*w12 + 2 = 0
     MEM (id: 1, read at: EXPR [ (1, w12) 0 ], value: EXPR [ (1, w13) 0 ])
-    EXPR w4 + -1*w9 = 0
-    EXPR w5 + -1*w11 = 0
-    EXPR w6 + -1*w13 = 0
+    EXPR w4 - w9 = 0
+    EXPR w5 - w11 = 0
+    EXPR w6 - w13 = 0
     ");
 }
 
@@ -161,9 +161,9 @@ fn generates_predicated_index_for_dynamic_read() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR w3*w4 + -1*w5 = 0
+    EXPR w3*w4 - w5 = 0
     MEM (id: 0, read at: EXPR [ (1, w5) 0 ], value: EXPR [ (1, w6) 0 ])
-    EXPR w6 + -10 = 0
+    EXPR w6 - 10 = 0
     ");
 }
 
@@ -199,10 +199,10 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR w3*w4 + -1*w8 = 0
+    EXPR w3*w4 - w8 = 0
     MEM (id: 0, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ])
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
-    EXPR -1*w4*w9 + 10*w4 + w9 + -1*w10 = 0
+    EXPR -1*w4*w9 + 10*w4 + w9 - w10 = 0
     MEM (id: 1, write EXPR [ (1, w10) 0 ] at: EXPR [ (1, w8) 0 ])
     EXPR -1*w11 = 0
     MEM (id: 1, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w12) 0 ])
@@ -210,9 +210,9 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     MEM (id: 1, read at: EXPR [ (1, w13) 0 ], value: EXPR [ (1, w14) 0 ])
     EXPR -1*w15 + 2 = 0
     MEM (id: 1, read at: EXPR [ (1, w15) 0 ], value: EXPR [ (1, w16) 0 ])
-    EXPR w5 + -1*w12 = 0
-    EXPR w6 + -1*w14 = 0
-    EXPR w7 + -1*w16 = 0
+    EXPR w5 - w12 = 0
+    EXPR w6 - w14 = 0
+    EXPR w7 - w16 = 0
     ");
 }
 
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index b231e6ea74d..10bf89815a3 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -153,22 +153,22 @@ fn multiple_brillig_stdlib_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
-    EXPR w1*w3 + -1 = 0
+    EXPR w1*w3 - 1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 + -1*w5 + -1*w6 + -1 = 0
+    EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + w0 + -1*w5 = 0
+    EXPR -1*w1*w4 + w0 - w5 = 0
     EXPR -1*w2 + w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w7]
-    EXPR w2*w7 + -1 = 0
+    EXPR w2*w7 - 1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w8, w9]
     BLACKBOX::RANGE [w9]:32 bits []
-    EXPR w2 + -1*w9 + -1*w10 + -1 = 0
+    EXPR w2 - w9 - w10 - 1 = 0
     BLACKBOX::RANGE [w10]:32 bits []
-    EXPR -1*w2*w8 + w1 + -1*w9 = 0
-    EXPR w8 + -1 = 0
+    EXPR -1*w2*w8 + w1 - w9 = 0
+    EXPR w8 - 1 = 0
 
     unconstrained func 0
     0: @21 = const u32 1
@@ -241,26 +241,26 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
-    EXPR w1*w3 + -1 = 0
+    EXPR w1*w3 - 1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 + -1*w5 + -1*w6 + -1 = 0
+    EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + w0 + -1*w5 = 0
+    EXPR -1*w1*w4 + w0 - w5 = 0
     EXPR -1*w2 + w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
     BLACKBOX::RANGE [w8]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w9]
-    EXPR w2*w9 + -1 = 0
+    EXPR w2*w9 - 1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w10, w11]
     BLACKBOX::RANGE [w11]:32 bits []
-    EXPR w2 + -1*w11 + -1*w12 + -1 = 0
+    EXPR w2 - w11 - w12 - 1 = 0
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR -1*w2*w10 + w1 + -1*w11 = 0
-    EXPR w10 + -1 = 0
+    EXPR -1*w2*w10 + w1 - w11 = 0
+    EXPR w10 - 1 = 0
 
     unconstrained func 0
      0: @2 = const u32 1
@@ -375,13 +375,13 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
-    EXPR w1*w3 + -1 = 0
+    EXPR w1*w3 - 1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 + -1*w5 + -1*w6 + -1 = 0
+    EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + w0 + -1*w5 = 0
+    EXPR -1*w1*w4 + w0 - w5 = 0
     EXPR -1*w2 + w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
@@ -390,13 +390,13 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w9]
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w10]
-    EXPR w2*w10 + -1 = 0
+    EXPR w2*w10 - 1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w11, w12]
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR w2 + -1*w12 + -1*w13 + -1 = 0
+    EXPR w2 - w12 - w13 - 1 = 0
     BLACKBOX::RANGE [w13]:32 bits []
-    EXPR -1*w2*w11 + w1 + -1*w12 = 0
-    EXPR w11 + -1 = 0
+    EXPR -1*w2*w11 + w1 - w12 = 0
+    EXPR w11 - 1 = 0
 
     func 1
     current witness: w5
@@ -405,9 +405,9 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR w0 + -1*w1 + -1*w3 = 0
+    EXPR w0 - w1 - w3 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w3) 0 ]], outputs: [w4]
-    EXPR w3*w4 + w5 + -1 = 0
+    EXPR w3*w4 + w5 - 1 = 0
     EXPR w3*w5 = 0
     EXPR w5 = 0
     EXPR -1*w0 + w2 = 0
diff --git a/compiler/noirc_evaluator/src/acir/tests/call.rs b/compiler/noirc_evaluator/src/acir/tests/call.rs
index 5884e36785a..9a876850291 100644
--- a/compiler/noirc_evaluator/src/acir/tests/call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/call.rs
@@ -64,14 +64,14 @@ fn basic_call_with_outputs_assert(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR w2 + -1*w3 = 0
+    EXPR w2 - w3 = 0
 
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 + -1*w1 = 0
+    EXPR w0 - w1 = 0
     EXPR -1*w0 + w2 = 0
     ");
 }
@@ -107,14 +107,14 @@ fn call_output_as_next_call_input(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w2, w1], outputs: [w3]
-    EXPR w2 + -1*w3 = 0
+    EXPR w2 - w3 = 0
 
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 + -1*w1 = 0
+    EXPR w0 - w1 = 0
     EXPR -1*w0 + w2 = 0
     ");
 }
@@ -154,24 +154,24 @@ fn basic_nested_call(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR w2 + -1*w3 = 0
+    EXPR w2 - w3 = 0
 
     func 1
     current witness: w4
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 + -1*w3 + 2 = 0
+    EXPR w0 - w3 + 2 = 0
     CALL func 2: PREDICATE: EXPR [ 1 ]
     inputs: [w3, w1], outputs: [w4]
-    EXPR w2 + -1*w4 = 0
+    EXPR w2 - w4 = 0
 
     func 2
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 + -1*w1 = 0
+    EXPR w0 - w1 = 0
     EXPR -1*w0 + w2 = 0
     ");
 }

From 8a2e7bbc6840380d11b76998bef77c3e97d1c20a Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 12:47:15 -0300
Subject: [PATCH 05/25] Witness equality to constant

---
 acvm-repo/acir/src/circuit/opcodes.rs         | 15 +++++++++
 acvm-repo/acir/src/parser/mod.rs              | 32 +++++++++++++------
 acvm-repo/acir/src/parser/tests.rs            |  8 ++---
 .../noirc_evaluator/src/acir/tests/arrays.rs  |  4 +--
 .../src/acir/tests/brillig_call.rs            |  6 ++--
 5 files changed, 46 insertions(+), 19 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index b1c200aa384..ebb27bc9f1e 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -149,6 +149,21 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
             Opcode::AssertZero(expr) => {
                 write!(f, "EXPR ")?;
 
+                // Check if it's `wN - C = 0` and print it as `wN = C`,
+                // or if its' `wN + C = 0` and print it as `wN = -C`.
+                if expr.mul_terms.is_empty() && expr.linear_combinations.len() == 1 {
+                    let (coefficient, witness) = expr.linear_combinations[0];
+                    let constant = expr.q_c;
+
+                    if coefficient.is_one() {
+                        // This is `wN + C = 0`, so show it as `wN = -C`.
+
+                        let constant = -constant;
+                        write!(f, "{witness} = {constant}")?;
+                        return Ok(());
+                    }
+                }
+
                 let mut printed_term = false;
 
                 for (coefficient, witness1, witness2) in &expr.mul_terms {
diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index 61aea113f73..c6faf399692 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -272,12 +272,22 @@ impl<'a> Parser<'a> {
         let mut mul_terms = Vec::new();
         let mut constant: Option<FieldElement> = None;
         let mut negative = false;
+        let mut first = true;
 
         loop {
             if let Some(w1) = self.eat_witness()? {
                 let coefficient = FieldElement::one();
                 let coefficient = if negative { -coefficient } else { coefficient };
 
+                if first && self.eat(Token::Equal)? {
+                    let q_c = self.eat_field_or_error()?;
+
+                    // Here we parsed `coefficient*witness = constant` so we produce `coefficient*witness - q_c = 0`
+                    linear_combinations.push((coefficient, w1));
+                    constant = Some(-q_c);
+                    break;
+                }
+
                 if self.eat(Token::Star)? {
                     let w2 = self.eat_witness_or_error()?;
                     mul_terms.push((coefficient, w1, w2));
@@ -309,6 +319,8 @@ impl<'a> Parser<'a> {
                 return self.expected_field_element();
             }
 
+            first = false;
+
             if self.eat(Token::Plus)? {
                 negative = false;
                 continue;
@@ -320,22 +332,22 @@ impl<'a> Parser<'a> {
             }
 
             if self.eat(Token::Equal)? {
+                let zero_token = self.token.token().clone();
+                let span = self.token.span();
+                let Some(zero) = self.eat_field_element()? else {
+                    return self.expected_field_element();
+                };
+
+                if !zero.is_zero() {
+                    return Err(ParserError::ExpectedZero { found: zero_token, span });
+                }
+
                 break;
             }
 
             return self.expected_token(Token::Equal);
         }
 
-        let zero_token = self.token.token().clone();
-        let span = self.token.span();
-        let Some(zero) = self.eat_field_element()? else {
-            return self.expected_field_element();
-        };
-
-        if !zero.is_zero() {
-            return Err(ParserError::ExpectedZero { found: zero_token, span });
-        }
-
         // If a constant isn't provided, we default it to zero
         let q_c = constant.unwrap_or_default();
 
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 353d3e794af..b8569169ba9 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -149,7 +149,7 @@ fn xor() {
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::XOR [w0, w1]:32 bits [w2]
-    EXPR w2 - 15 = 0
+    EXPR w2 = 15
     ";
     assert_circuit_roundtrip(src);
 }
@@ -613,9 +613,9 @@ fn array_dynamic() {
     EXPR w20 - w21 - 5 = 0
     EXPR w21 - w22 - 3 = 0
     MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w23) 0 ])
-    EXPR w23 - 111 = 0
+    EXPR w23 = 111
     MEM (id: 0, read at: EXPR [ (1, w22) 0 ], value: EXPR [ (1, w24) 0 ])
-    EXPR w24 - 101 = 0
+    EXPR w24 = 101
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w22) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w25, w26]
     BLACKBOX::RANGE [w26]:32 bits []
     EXPR w22 - 4294967296*w25 - w26 + 4294967291 = 0
@@ -623,7 +623,7 @@ fn array_dynamic() {
     EXPR -1*w27 = 0
     MEM (id: 0, write EXPR [ (1, w27) 0 ] at: EXPR [ (1, w22) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w28) 0 ])
-    EXPR w28 - 111 = 0
+    EXPR w28 = 111
     EXPR -1*w29 + 1 = 0
     MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w30) 0 ])
     EXPR w30 = 0
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index 0f7f54b63a3..c7f148bbbd4 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -97,7 +97,7 @@ fn generates_memory_op_for_dynamic_read() {
     return values: []
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     MEM (id: 0, read at: EXPR [ (1, w3) 0 ], value: EXPR [ (1, w4) 0 ])
-    EXPR w4 - 10 = 0
+    EXPR w4 = 10
     ");
 }
 
@@ -163,7 +163,7 @@ fn generates_predicated_index_for_dynamic_read() {
     BLACKBOX::RANGE [w4]:1 bits []
     EXPR w3*w4 - w5 = 0
     MEM (id: 0, read at: EXPR [ (1, w5) 0 ], value: EXPR [ (1, w6) 0 ])
-    EXPR w6 - 10 = 0
+    EXPR w6 = 10
     ");
 }
 
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index 10bf89815a3..68a556d854a 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -168,7 +168,7 @@ fn multiple_brillig_stdlib_calls() {
     EXPR w2 - w9 - w10 - 1 = 0
     BLACKBOX::RANGE [w10]:32 bits []
     EXPR -1*w2*w8 + w1 - w9 = 0
-    EXPR w8 - 1 = 0
+    EXPR w8 = 1
 
     unconstrained func 0
     0: @21 = const u32 1
@@ -260,7 +260,7 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     EXPR w2 - w11 - w12 - 1 = 0
     BLACKBOX::RANGE [w12]:32 bits []
     EXPR -1*w2*w10 + w1 - w11 = 0
-    EXPR w10 - 1 = 0
+    EXPR w10 = 1
 
     unconstrained func 0
      0: @2 = const u32 1
@@ -396,7 +396,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     EXPR w2 - w12 - w13 - 1 = 0
     BLACKBOX::RANGE [w13]:32 bits []
     EXPR -1*w2*w11 + w1 - w12 = 0
-    EXPR w11 - 1 = 0
+    EXPR w11 = 1
 
     func 1
     current witness: w5

From e4e358c74f9771fc4ddceda972f504416d51bf8f Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 12:52:16 -0300
Subject: [PATCH 06/25] Another witness equality to constant

---
 acvm-repo/acir/src/circuit/opcodes.rs         |  7 +++++-
 acvm-repo/acir/src/parser/tests.rs            | 22 +++++++++----------
 .../noirc_evaluator/src/acir/tests/arrays.rs  | 20 ++++++++---------
 3 files changed, 27 insertions(+), 22 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index ebb27bc9f1e..f7459f9b283 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -157,11 +157,16 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
 
                     if coefficient.is_one() {
                         // This is `wN + C = 0`, so show it as `wN = -C`.
-
                         let constant = -constant;
                         write!(f, "{witness} = {constant}")?;
                         return Ok(());
                     }
+
+                    if (-coefficient).is_one() {
+                        // This is `-wN + C = 0`, so show it as `wN = C`.
+                        write!(f, "{witness} = {constant}")?;
+                        return Ok(());
+                    }
                 }
 
                 let mut printed_term = false;
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index b8569169ba9..84d6f0920ad 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -619,12 +619,12 @@ fn array_dynamic() {
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w22) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w25, w26]
     BLACKBOX::RANGE [w26]:32 bits []
     EXPR w22 - 4294967296*w25 - w26 + 4294967291 = 0
-    EXPR -1*w25 = 0
-    EXPR -1*w27 = 0
+    EXPR w25 = 0
+    EXPR w27 = 0
     MEM (id: 0, write EXPR [ (1, w27) 0 ] at: EXPR [ (1, w22) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w28) 0 ])
     EXPR w28 = 111
-    EXPR -1*w29 + 1 = 0
+    EXPR w29 = 1
     MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w30) 0 ])
     EXPR w30 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967286 ], EXPR [ 4294967296 ]], outputs: [w31, w32]
@@ -644,11 +644,11 @@ fn array_dynamic() {
     MEM (id: 0, read at: EXPR [ (1, w38) 0 ], value: EXPR [ (1, w39) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w27) 0 ], value: EXPR [ (1, w40) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w41) 0 ])
-    EXPR -1*w42 + 2 = 0
+    EXPR w42 = 2
     MEM (id: 0, read at: EXPR [ (1, w42) 0 ], value: EXPR [ (1, w43) 0 ])
-    EXPR -1*w44 + 3 = 0
+    EXPR w44 = 3
     MEM (id: 0, read at: EXPR [ (1, w44) 0 ], value: EXPR [ (1, w45) 0 ])
-    EXPR -1*w46 + 4 = 0
+    EXPR w46 = 0
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w47) 0 ])
     INIT (id: 3, len: 5, witnesses: [w40, w41, w43, w45, w47])
     EXPR -1*w31*w35 + w31*w39 + w35 - w48 = 0
@@ -664,11 +664,11 @@ fn array_dynamic() {
     EXPR -1*w31 - w55 + 1 = 0
     EXPR -1*w31*w49 + w31*w50 + w49 - w56 = 0
     EXPR w31*w54 + w55*w56 - 109 = 0
-    EXPR -1*w57 + 246 = 0
-    EXPR -1*w58 + 159 = 0
-    EXPR -1*w59 + 32 = 0
-    EXPR -1*w60 + 176 = 0
-    EXPR -1*w61 + 8 = 0
+    EXPR w57 = 246
+    EXPR w58 = 159
+    EXPR w59 = 32
+    EXPR w60 = 176
+    EXPR w61 = 8
     INIT (id: 4, len: 5, witnesses: [w57, w58, w59, w60, w61])
     MEM (id: 4, read at: EXPR [ (1, w7) 0 ], value: EXPR [ (1, w62) 0 ])
     MEM (id: 4, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w63) 0 ])
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index c7f148bbbd4..6925321ee2b 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -49,10 +49,10 @@ fn constant_array_access_out_of_bounds() {
     private parameters: []
     public parameters: []
     return values: []
-    EXPR -1*w0 = 0
-    EXPR -1*w1 + 1 = 0
+    EXPR w0 = 0
+    EXPR w1 = 1
     INIT (id: 0, len: 2, witnesses: [w0, w1])
-    EXPR -1*w2 + 5 = 0
+    EXPR w2 = 5
     MEM (id: 0, read at: EXPR [ (1, w2) 0 ], value: EXPR [ (1, w3) 0 ])
     EXPR w3 = 0
     ");
@@ -120,13 +120,13 @@ fn generates_memory_op_for_dynamic_write() {
     public parameters: []
     return values: [w4, w5, w6]
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
-    EXPR -1*w7 + 10 = 0
+    EXPR w7 = 10
     MEM (id: 1, write EXPR [ (1, w7) 0 ] at: EXPR [ (1, w3) 0 ])
-    EXPR -1*w8 = 0
+    EXPR w8 = 0
     MEM (id: 1, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ])
-    EXPR -1*w10 + 1 = 0
+    EXPR w10 = 1
     MEM (id: 1, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w11) 0 ])
-    EXPR -1*w12 + 2 = 0
+    EXPR w12 = 2
     MEM (id: 1, read at: EXPR [ (1, w12) 0 ], value: EXPR [ (1, w13) 0 ])
     EXPR w4 - w9 = 0
     EXPR w5 - w11 = 0
@@ -204,11 +204,11 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
     EXPR -1*w4*w9 + 10*w4 + w9 - w10 = 0
     MEM (id: 1, write EXPR [ (1, w10) 0 ] at: EXPR [ (1, w8) 0 ])
-    EXPR -1*w11 = 0
+    EXPR w11 = 0
     MEM (id: 1, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w12) 0 ])
-    EXPR -1*w13 + 1 = 0
+    EXPR w13 = 1
     MEM (id: 1, read at: EXPR [ (1, w13) 0 ], value: EXPR [ (1, w14) 0 ])
-    EXPR -1*w15 + 2 = 0
+    EXPR w15 = 2
     MEM (id: 1, read at: EXPR [ (1, w15) 0 ], value: EXPR [ (1, w16) 0 ])
     EXPR w5 - w12 = 0
     EXPR w6 - w14 = 0

From 8b0e22c487fc4ca5996cec360070ab34670f527c Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 12:58:01 -0300
Subject: [PATCH 07/25] Handle `-1` in first term

---
 acvm-repo/acir/src/circuit/opcodes.rs         |  4 ++
 acvm-repo/acir/src/parser/mod.rs              |  2 +-
 acvm-repo/acir/src/parser/tests.rs            | 68 +++++++++----------
 .../noirc_evaluator/src/acir/tests/arrays.rs  |  2 +-
 .../src/acir/tests/brillig_call.rs            | 20 +++---
 .../noirc_evaluator/src/acir/tests/call.rs    |  6 +-
 .../noirc_evaluator/src/acir/tests/mod.rs     |  2 +-
 7 files changed, 54 insertions(+), 50 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index f7459f9b283..bdbb92fe730 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -191,6 +191,8 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
 
                     if coefficient.is_one() {
                         write!(f, "{witness1}*{witness2}")?;
+                    } else if (-coefficient).is_one() {
+                        write!(f, "-{witness1}*{witness2}")?;
                     } else {
                         write!(f, "{coefficient}*{witness1}*{witness2}")?;
                     }
@@ -218,6 +220,8 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
 
                     if coefficient.is_one() {
                         write!(f, "{witness}")?;
+                    } else if (-coefficient).is_one() {
+                        write!(f, "-{witness}")?;
                     } else {
                         write!(f, "{coefficient}*{witness}")?;
                     }
diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index c6faf399692..ce7e734ce88 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -271,8 +271,8 @@ impl<'a> Parser<'a> {
         let mut linear_combinations = Vec::new();
         let mut mul_terms = Vec::new();
         let mut constant: Option<FieldElement> = None;
-        let mut negative = false;
         let mut first = true;
+        let mut negative = self.eat(Token::Minus)?;
 
         loop {
             if let Some(w1) = self.eat_witness()? {
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 84d6f0920ad..a084369a318 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -122,7 +122,7 @@ fn assert_zero_with_mul_terms() {
     EXPR w3*w3 - w4 = 0
     EXPR w4*w4 - w5 = 0
     EXPR w5*w5 - w6 = 0
-    EXPR -1*w2 + w6 = 0
+    EXPR -w2 + w6 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -223,22 +223,22 @@ fn aes128_encrypt() {
     BLACKBOX::RANGE [w58]:8 bits []
     BLACKBOX::RANGE [w59]:8 bits []
     BLACKBOX::AES128_ENCRYPT [w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43] [w60, w61, w62, w63, w64, w65, w66, w67, w68, w69, w70, w71, w72, w73, w74, w75]
-    EXPR -1*w44 + w60 = 0
-    EXPR -1*w45 + w61 = 0
-    EXPR -1*w46 + w62 = 0
-    EXPR -1*w47 + w63 = 0
-    EXPR -1*w48 + w64 = 0
-    EXPR -1*w49 + w65 = 0
-    EXPR -1*w50 + w66 = 0
-    EXPR -1*w51 + w67 = 0
-    EXPR -1*w52 + w68 = 0
-    EXPR -1*w53 + w69 = 0
-    EXPR -1*w54 + w70 = 0
-    EXPR -1*w55 + w71 = 0
-    EXPR -1*w56 + w72 = 0
-    EXPR -1*w57 + w73 = 0
-    EXPR -1*w58 + w74 = 0
-    EXPR -1*w59 + w75 = 0
+    EXPR -w44 + w60 = 0
+    EXPR -w45 + w61 = 0
+    EXPR -w46 + w62 = 0
+    EXPR -w47 + w63 = 0
+    EXPR -w48 + w64 = 0
+    EXPR -w49 + w65 = 0
+    EXPR -w50 + w66 = 0
+    EXPR -w51 + w67 = 0
+    EXPR -w52 + w68 = 0
+    EXPR -w53 + w69 = 0
+    EXPR -w54 + w70 = 0
+    EXPR -w55 + w71 = 0
+    EXPR -w56 + w72 = 0
+    EXPR -w57 + w73 = 0
+    EXPR -w58 + w74 = 0
+    EXPR -w59 + w75 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -526,7 +526,7 @@ fn brillig_call() {
     return values: []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
-    EXPR -1*w0 + w2 = 0
+    EXPR -w0 + w2 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -541,7 +541,7 @@ fn brillig_call_with_predicate() {
     BRILLIG CALL func 0: PREDICATE: EXPR [ 1 ]
     inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
-    EXPR -1*w0 + w2 = 0
+    EXPR -w0 + w2 = 0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -631,16 +631,16 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w31]:1 bits []
     BLACKBOX::RANGE [w32]:32 bits []
     EXPR w21 - 4294967296*w31 - w32 + 4294967286 = 0
-    EXPR -1*w21*w31 + w21 - w33 = 0
+    EXPR -w21*w31 + w21 - w33 = 0
     MEM (id: 0, read at: EXPR [ (1, w33) 0 ], value: EXPR [ (1, w34) 0 ])
-    EXPR -1*w31*w34 + 2*w31 + w34 - w35 - 2 = 0
+    EXPR -w31*w34 + 2*w31 + w34 - w35 - 2 = 0
     BLACKBOX::RANGE [w35]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w36, w37]
     BLACKBOX::RANGE [w36]:1 bits []
     BLACKBOX::RANGE [w37]:32 bits []
     EXPR w21 - 4294967296*w36 - w37 + 4294967291 = 0
     EXPR w31*w36 - w36 = 0
-    EXPR -1*w21*w31 + w21 - w38 = 0
+    EXPR -w21*w31 + w21 - w38 = 0
     MEM (id: 0, read at: EXPR [ (1, w38) 0 ], value: EXPR [ (1, w39) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w27) 0 ], value: EXPR [ (1, w40) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w41) 0 ])
@@ -651,18 +651,18 @@ fn array_dynamic() {
     EXPR w46 = 0
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w47) 0 ])
     INIT (id: 3, len: 5, witnesses: [w40, w41, w43, w45, w47])
-    EXPR -1*w31*w35 + w31*w39 + w35 - w48 = 0
+    EXPR -w31*w35 + w31*w39 + w35 - w48 = 0
     MEM (id: 3, write EXPR [ (1, w48) 0 ] at: EXPR [ (1, w38) 0 ])
     MEM (id: 3, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w49) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w50) 0 ])
-    EXPR -1*w31*w36 = 0
+    EXPR -w31*w36 = 0
     EXPR w21*w31 - w51 = 0
     MEM (id: 0, read at: EXPR [ (1, w51) 0 ], value: EXPR [ (1, w52) 0 ])
-    EXPR -1*w31*w52 + w52 - w53 = 0
+    EXPR -w31*w52 + w52 - w53 = 0
     MEM (id: 0, write EXPR [ (1, w53) 0 ] at: EXPR [ (1, w51) 0 ])
     MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w54) 0 ])
-    EXPR -1*w31 - w55 + 1 = 0
-    EXPR -1*w31*w49 + w31*w50 + w49 - w56 = 0
+    EXPR -w31 - w55 + 1 = 0
+    EXPR -w31*w49 + w31*w50 + w49 - w56 = 0
     EXPR w31*w54 + w55*w56 - 109 = 0
     EXPR w57 = 246
     EXPR w58 = 159
@@ -681,20 +681,20 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w68]:222 bits []
     BLACKBOX::RANGE [w69]:32 bits []
     EXPR w18 - 4294967296*w68 - w69 = 0
-    EXPR -1*w68 - w70 + 5096253676302562286669017222071363378443840053029366383258766538131 = 0
+    EXPR -w68 - w70 + 5096253676302562286669017222071363378443840053029366383258766538131 = 0
     BLACKBOX::RANGE [w70]:222 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (-1, w68) 5096253676302562286669017222071363378443840053029366383258766538131 ]], outputs: [w71]
-    EXPR -1*w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + w72 - 1 = 0
-    EXPR -1*w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72 = 0
+    EXPR -w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + w72 - 1 = 0
+    EXPR -w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72 = 0
     EXPR w69*w72 + 268435455*w72 - w73 = 0
     BLACKBOX::RANGE [w73]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (-1, w69) 4294967299 ], EXPR [ 4294967296 ]], outputs: [w74, w75]
     BLACKBOX::RANGE [w74]:1 bits []
     BLACKBOX::RANGE [w75]:32 bits []
-    EXPR -1*w69 - 4294967296*w74 - w75 + 4294967299 = 0
-    EXPR -1*w17*w74 + w17 - 3*w74 - w76 + 3 = 0
+    EXPR -w69 - 4294967296*w74 - w75 + 4294967299 = 0
+    EXPR -w17*w74 + w17 - 3*w74 - w76 + 3 = 0
     BLACKBOX::RANGE [w76]:32 bits []
-    EXPR -1*w74*w76 + w76 - w77 = 0
+    EXPR -w74*w76 + w76 - w77 = 0
     MEM (id: 1, read at: EXPR [ (1, w77) 0 ], value: EXPR [ (1, w78) 0 ])
     EXPR w15*w74 - w74*w78 - w15 + w78 = 0
     ";
@@ -719,7 +719,7 @@ fn fold_basic() {
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
-    EXPR -1*w0 + w2 = 0
+    EXPR -w0 + w2 = 0
     ";
     assert_program_roundtrip(src);
 }
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index 6925321ee2b..9e3face0bab 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -202,7 +202,7 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     EXPR w3*w4 - w8 = 0
     MEM (id: 0, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ])
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
-    EXPR -1*w4*w9 + 10*w4 + w9 - w10 = 0
+    EXPR -w4*w9 + 10*w4 + w9 - w10 = 0
     MEM (id: 1, write EXPR [ (1, w10) 0 ] at: EXPR [ (1, w8) 0 ])
     EXPR w11 = 0
     MEM (id: 1, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w12) 0 ])
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index 68a556d854a..bfe76a47592 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -159,15 +159,15 @@ fn multiple_brillig_stdlib_calls() {
     BLACKBOX::RANGE [w5]:32 bits []
     EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + w0 - w5 = 0
-    EXPR -1*w2 + w4 = 0
+    EXPR -w1*w4 + w0 - w5 = 0
+    EXPR -w2 + w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w7]
     EXPR w2*w7 - 1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w8, w9]
     BLACKBOX::RANGE [w9]:32 bits []
     EXPR w2 - w9 - w10 - 1 = 0
     BLACKBOX::RANGE [w10]:32 bits []
-    EXPR -1*w2*w8 + w1 - w9 = 0
+    EXPR -w2*w8 + w1 - w9 = 0
     EXPR w8 = 1
 
     unconstrained func 0
@@ -247,8 +247,8 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BLACKBOX::RANGE [w5]:32 bits []
     EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + w0 - w5 = 0
-    EXPR -1*w2 + w4 = 0
+    EXPR -w1*w4 + w0 - w5 = 0
+    EXPR -w2 + w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
@@ -259,7 +259,7 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BLACKBOX::RANGE [w11]:32 bits []
     EXPR w2 - w11 - w12 - 1 = 0
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR -1*w2*w10 + w1 - w11 = 0
+    EXPR -w2*w10 + w1 - w11 = 0
     EXPR w10 = 1
 
     unconstrained func 0
@@ -381,8 +381,8 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w5]:32 bits []
     EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -1*w1*w4 + w0 - w5 = 0
-    EXPR -1*w2 + w4 = 0
+    EXPR -w1*w4 + w0 - w5 = 0
+    EXPR -w2 + w4 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
@@ -395,7 +395,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w12]:32 bits []
     EXPR w2 - w12 - w13 - 1 = 0
     BLACKBOX::RANGE [w13]:32 bits []
-    EXPR -1*w2*w11 + w1 - w12 = 0
+    EXPR -w2*w11 + w1 - w12 = 0
     EXPR w11 = 1
 
     func 1
@@ -410,7 +410,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     EXPR w3*w4 + w5 - 1 = 0
     EXPR w3*w5 = 0
     EXPR w5 = 0
-    EXPR -1*w0 + w2 = 0
+    EXPR -w0 + w2 = 0
 
     unconstrained func 0
      0: @2 = const u32 1
diff --git a/compiler/noirc_evaluator/src/acir/tests/call.rs b/compiler/noirc_evaluator/src/acir/tests/call.rs
index 9a876850291..5eca1363d05 100644
--- a/compiler/noirc_evaluator/src/acir/tests/call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/call.rs
@@ -72,7 +72,7 @@ fn basic_call_with_outputs_assert(inline_type: InlineType) {
     public parameters: []
     return values: [w2]
     EXPR w0 - w1 = 0
-    EXPR -1*w0 + w2 = 0
+    EXPR -w0 + w2 = 0
     ");
 }
 
@@ -115,7 +115,7 @@ fn call_output_as_next_call_input(inline_type: InlineType) {
     public parameters: []
     return values: [w2]
     EXPR w0 - w1 = 0
-    EXPR -1*w0 + w2 = 0
+    EXPR -w0 + w2 = 0
     ");
 }
 
@@ -172,6 +172,6 @@ fn basic_nested_call(inline_type: InlineType) {
     public parameters: []
     return values: [w2]
     EXPR w0 - w1 = 0
-    EXPR -1*w0 + w2 = 0
+    EXPR -w0 + w2 = 0
     ");
 }
diff --git a/compiler/noirc_evaluator/src/acir/tests/mod.rs b/compiler/noirc_evaluator/src/acir/tests/mod.rs
index 088b42b246e..a72290ce958 100644
--- a/compiler/noirc_evaluator/src/acir/tests/mod.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/mod.rs
@@ -95,7 +95,7 @@ fn unchecked_mul_should_not_have_range_check() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR -1*w0*w1 + w2 = 0
+    EXPR -w0*w1 + w2 = 0
     ");
 }
 

From 91eed2c6597df7a5dbc1cd81c30c4d1e3e858b7c Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 13:11:21 -0300
Subject: [PATCH 08/25] Stop parsing the old way

---
 acvm-repo/acir/src/parser/mod.rs              |  9 ---------
 acvm-repo/acir/src/parser/tests.rs            |  4 ++--
 .../acvm/src/compiler/optimizers/general.rs   | 12 +++++------
 .../compiler/optimizers/merge_expressions.rs  | 20 +++++++++----------
 .../compiler/optimizers/redundant_range.rs    | 12 +++++------
 5 files changed, 24 insertions(+), 33 deletions(-)

diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index ce7e734ce88..5d4d4e69d16 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -263,11 +263,6 @@ impl<'a> Parser<'a> {
     fn parse_assert_zero_expression(&mut self) -> ParseResult<Expression<FieldElement>> {
         self.eat_keyword_or_error(Keyword::Expression)?;
 
-        // Support the old `EXPR [ ... ]` syntax for old tests, for now
-        if matches!(self.token.token(), Token::LeftBracket) {
-            return self.parse_arithmetic_expression_after_expr();
-        }
-
         let mut linear_combinations = Vec::new();
         let mut mul_terms = Vec::new();
         let mut constant: Option<FieldElement> = None;
@@ -356,10 +351,6 @@ impl<'a> Parser<'a> {
 
     fn parse_arithmetic_expression(&mut self) -> ParseResult<Expression<FieldElement>> {
         self.eat_keyword_or_error(Keyword::Expression)?;
-        self.parse_arithmetic_expression_after_expr()
-    }
-
-    fn parse_arithmetic_expression_after_expr(&mut self) -> ParseResult<Expression<FieldElement>> {
         self.eat_or_error(Token::LeftBracket)?;
 
         let mut linear_combinations = Vec::new();
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index a084369a318..05c6d99da3e 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -741,8 +741,8 @@ fn fold_basic_mismatched_ids() {
     public parameters: []
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
-    EXPR [ (1, w0, w3) (-1, w1, w3) -1 ]
-    EXPR [ (-1, w0) (1, w2) 0 ]
+    EXPR w0*w3 - w1*w3 - 1 = 0
+    EXPR -w0 + w2 = 0
     ";
     let result = Program::from_str(src).err().unwrap();
     let ParserError::UnexpectedFunctionId { expected, found, .. } = result.get_error() else {
diff --git a/acvm-repo/acvm/src/compiler/optimizers/general.rs b/acvm-repo/acvm/src/compiler/optimizers/general.rs
index e28f7bf95d1..4a8d3dbc9d1 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/general.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/general.rs
@@ -93,7 +93,7 @@ mod tests {
         return values: []
 
         // The first multiplication should be removed
-        EXPR [ (0, w0, w1) (1, w0, w1) 0 ]
+        EXPR 0*w0*w1 + w0*w1 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
         let optimized_circuit = optimize(circuit);
@@ -115,7 +115,7 @@ mod tests {
         return values: []
 
         // The first linear combination should be removed
-        EXPR [ (0, w0) (1, w1) 0 ]
+        EXPR 0*w0 + w1 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
         let optimized_circuit = optimize(circuit);
@@ -138,7 +138,7 @@ mod tests {
 
         // There are all mul terms with the same variables so we should end up with just one
         // that is the sum of all the coefficients
-        EXPR [ (2, w0, w1) (3, w1, w0) (4, w0, w1) 0 ]
+        EXPR 2*w0*w1 + 3*w1*w0 + 4*w0*w1 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
         let optimized_circuit = optimize(circuit);
@@ -158,7 +158,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR [ (2, w0, w1) (3, w1, w0) (-5, w0, w1) 0 ]
+        EXPR 2*w0*w1 + 3*w1*w0 - 5*w0*w1 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
         let optimized_circuit = optimize(circuit);
@@ -181,7 +181,7 @@ mod tests {
 
         // These are all linear terms with the same variable so we should end up with just one
         // that is the sum of all the coefficients
-        EXPR [ (1, w0) (2, w0) (3, w0) 0 ]
+        EXPR w0 + 2*w0 + 3*w0 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
         let optimized_circuit = optimize(circuit);
@@ -201,7 +201,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR [ (1, w0) (2, w0) (-3, w0) 0 ]
+        EXPR w0 + 2*w0 - 3*w0 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
         let optimized_circuit = optimize(circuit);
diff --git a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
index 9d1d9134cd7..a74f07ca8a1 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
@@ -304,8 +304,8 @@ mod tests {
         public parameters: []
         return values: []
         BRILLIG CALL func 0: inputs: [], outputs: [w1]
-        EXPR [ (2, w0) (3, w1) (1, w2) 1 ]
-        EXPR [ (2, w0) (2, w1) (1, w5) 1 ]
+        EXPR 2*w0 + 3*w1 + w2 + 1 = 0
+        EXPR 2*w0 + 2*w1 + w5 + 1 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
         let optimized_circuit = merge_expressions(circuit.clone());
@@ -319,8 +319,8 @@ mod tests {
         private parameters: [w0]
         public parameters: []
         return values: [w1, w2]
-        EXPR [ (-1, w0, w0) (1, w1) 0 ]
-        EXPR [ (-1, w1) (1, w2) 0 ]
+        EXPR -w0*w0 + w1 = 0
+        EXPR -w1 + w2 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
         let optimized_circuit = merge_expressions(circuit.clone());
@@ -334,10 +334,10 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR [ (1, w0, w0) (-1, w4) 0 ]
-        EXPR [ (1, w0, w1) (1, w5) 0 ]
-        EXPR [ (-1, w2) (1, w4) (1, w5) 0 ]
-        EXPR [ (1, w2) (-1, w3) (1, w4) (1, w5) 0 ]
+        EXPR w0*w0 - w4 = 0
+        EXPR w0*w1 + w5 = 0
+        EXPR -w2 + w4 + w5 = 0
+        EXPR w2 - w3 + w4 + w5 = 0
         BLACKBOX::RANGE [w3]:32 bits []
         ";
         let circuit = Circuit::from_str(src).unwrap();
@@ -367,8 +367,8 @@ mod tests {
         return values: [w2]
         BRILLIG CALL func 0: inputs: [], outputs: [w3]
         BLACKBOX::AND [w0, w1]:8 bits [w4]
-        EXPR [ (1, w3) (-1, w4) 0 ]
-        EXPR [ (-1, w2) (1, w4) 0 ]
+        EXPR w3 - w4 = 0
+        EXPR -w2 + w4 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
         let optimized_circuit = merge_expressions(circuit.clone());
diff --git a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
index 131f6445de3..77126b0f5f9 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
@@ -349,10 +349,10 @@ mod tests {
         return values: []
         BLACKBOX::RANGE [w1]:16 bits []
         BLACKBOX::RANGE [w1]:16 bits []
-        EXPR [ 0 ]
-        EXPR [ 0 ]
-        EXPR [ 0 ]
-        EXPR [ 0 ]
+        EXPR 0 = 0
+        EXPR 0 = 0
+        EXPR 0 = 0
+        EXPR 0 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
 
@@ -382,7 +382,7 @@ mod tests {
         public parameters: []
         return values: []
         BLACKBOX::RANGE [w1]:16 bits []
-        EXPR [ (1, w1) 0 ]
+        EXPR w1 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
 
@@ -420,7 +420,7 @@ mod tests {
         BLACKBOX::RANGE [w1]:64 bits []
 
         // assert w1 == 0
-        EXPR [ (1, w1) 0 ]
+        EXPR w1 = 0
         ";
         let circuit = Circuit::from_str(src).unwrap();
 

From b06db65a8d109e6032c59c92521c80521afff8d3 Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 13:20:10 -0300
Subject: [PATCH 09/25] Special case for `w0 = w1`

---
 acvm-repo/acir/src/circuit/opcodes.rs         | 17 +++++++
 acvm-repo/acir/src/parser/mod.rs              |  9 +++-
 acvm-repo/acir/src/parser/tests.rs            | 50 +++++++++----------
 .../noirc_evaluator/src/acir/tests/arrays.rs  | 12 ++---
 .../src/acir/tests/brillig_call.rs            |  8 +--
 .../noirc_evaluator/src/acir/tests/call.rs    | 20 ++++----
 6 files changed, 70 insertions(+), 46 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index bdbb92fe730..c3513222e24 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -169,6 +169,23 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                     }
                 }
 
+                // Chec if it's `-wN * wM = 0` or `wN * -wM = 0` in which case we can
+                // print it as `wN = wM`.
+                if expr.mul_terms.is_empty()
+                    && expr.linear_combinations.len() == 2
+                    && expr.q_c.is_zero()
+                {
+                    let (coefficient1, witness1) = expr.linear_combinations[0];
+                    let (coefficient2, witness2) = expr.linear_combinations[1];
+
+                    if (coefficient1.is_one() && (-coefficient2).is_one())
+                        || ((-coefficient1).is_one() && coefficient2.is_one())
+                    {
+                        write!(f, "{witness1} = {witness2}")?;
+                        return Ok(());
+                    }
+                }
+
                 let mut printed_term = false;
 
                 for (coefficient, witness1, witness2) in &expr.mul_terms {
diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index 5d4d4e69d16..42610582398 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -275,9 +275,16 @@ impl<'a> Parser<'a> {
                 let coefficient = if negative { -coefficient } else { coefficient };
 
                 if first && self.eat(Token::Equal)? {
+                    if let Some(w2) = self.eat_witness()? {
+                        // Here we parsed `coefficient*w1 = w2` so we produce `coefficient*w1 - w2 = 0`
+                        linear_combinations.push((coefficient, w1));
+                        linear_combinations.push((-FieldElement::one(), w2));
+                        break;
+                    }
+
                     let q_c = self.eat_field_or_error()?;
 
-                    // Here we parsed `coefficient*witness = constant` so we produce `coefficient*witness - q_c = 0`
+                    // Here we parsed `coefficient*w1 = constant` so we produce `coefficient*w1 - q_c = 0`
                     linear_combinations.push((coefficient, w1));
                     constant = Some(-q_c);
                     break;
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 05c6d99da3e..cd2d57f70ef 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -102,11 +102,11 @@ fn assert_zero_opcodes() {
     private parameters: [w0, w1, w2, w3, w4]
     public parameters: [w5, w6, w7, w8, w9]
     return values: []
-    EXPR w0 - w5 = 0
-    EXPR w1 - w6 = 0
-    EXPR w2 - w7 = 0
-    EXPR w3 - w8 = 0
-    EXPR w4 - w9 = 0
+    EXPR w0 = w5
+    EXPR w1 = w6
+    EXPR w2 = w7
+    EXPR w3 = w8
+    EXPR w4 = w9
     ";
     assert_circuit_roundtrip(src);
 }
@@ -122,7 +122,7 @@ fn assert_zero_with_mul_terms() {
     EXPR w3*w3 - w4 = 0
     EXPR w4*w4 - w5 = 0
     EXPR w5*w5 - w6 = 0
-    EXPR -w2 + w6 = 0
+    EXPR w2 = w6
     ";
     assert_circuit_roundtrip(src);
 }
@@ -223,22 +223,22 @@ fn aes128_encrypt() {
     BLACKBOX::RANGE [w58]:8 bits []
     BLACKBOX::RANGE [w59]:8 bits []
     BLACKBOX::AES128_ENCRYPT [w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43] [w60, w61, w62, w63, w64, w65, w66, w67, w68, w69, w70, w71, w72, w73, w74, w75]
-    EXPR -w44 + w60 = 0
-    EXPR -w45 + w61 = 0
-    EXPR -w46 + w62 = 0
-    EXPR -w47 + w63 = 0
-    EXPR -w48 + w64 = 0
-    EXPR -w49 + w65 = 0
-    EXPR -w50 + w66 = 0
-    EXPR -w51 + w67 = 0
-    EXPR -w52 + w68 = 0
-    EXPR -w53 + w69 = 0
-    EXPR -w54 + w70 = 0
-    EXPR -w55 + w71 = 0
-    EXPR -w56 + w72 = 0
-    EXPR -w57 + w73 = 0
-    EXPR -w58 + w74 = 0
-    EXPR -w59 + w75 = 0
+    EXPR w44 = w60
+    EXPR w45 = w61
+    EXPR w46 = w62
+    EXPR w47 = w63
+    EXPR w48 = w64
+    EXPR w49 = w65
+    EXPR w50 = w66
+    EXPR w51 = w67
+    EXPR w52 = w68
+    EXPR w53 = w69
+    EXPR w54 = w70
+    EXPR w55 = w71
+    EXPR w56 = w72
+    EXPR w57 = w73
+    EXPR w58 = w74
+    EXPR w59 = w75
     ";
     assert_circuit_roundtrip(src);
 }
@@ -526,7 +526,7 @@ fn brillig_call() {
     return values: []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
-    EXPR -w0 + w2 = 0
+    EXPR w0 = w2
     ";
     assert_circuit_roundtrip(src);
 }
@@ -541,7 +541,7 @@ fn brillig_call_with_predicate() {
     BRILLIG CALL func 0: PREDICATE: EXPR [ 1 ]
     inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
-    EXPR -w0 + w2 = 0
+    EXPR w0 = w2
     ";
     assert_circuit_roundtrip(src);
 }
@@ -719,7 +719,7 @@ fn fold_basic() {
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
-    EXPR -w0 + w2 = 0
+    EXPR w0 = w2
     ";
     assert_program_roundtrip(src);
 }
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index 9e3face0bab..7579c054716 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -128,9 +128,9 @@ fn generates_memory_op_for_dynamic_write() {
     MEM (id: 1, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w11) 0 ])
     EXPR w12 = 2
     MEM (id: 1, read at: EXPR [ (1, w12) 0 ], value: EXPR [ (1, w13) 0 ])
-    EXPR w4 - w9 = 0
-    EXPR w5 - w11 = 0
-    EXPR w6 - w13 = 0
+    EXPR w4 = w9
+    EXPR w5 = w11
+    EXPR w6 = w13
     ");
 }
 
@@ -210,9 +210,9 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     MEM (id: 1, read at: EXPR [ (1, w13) 0 ], value: EXPR [ (1, w14) 0 ])
     EXPR w15 = 2
     MEM (id: 1, read at: EXPR [ (1, w15) 0 ], value: EXPR [ (1, w16) 0 ])
-    EXPR w5 - w12 = 0
-    EXPR w6 - w14 = 0
-    EXPR w7 - w16 = 0
+    EXPR w5 = w12
+    EXPR w6 = w14
+    EXPR w7 = w16
     ");
 }
 
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index bfe76a47592..a468340ea07 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -160,7 +160,7 @@ fn multiple_brillig_stdlib_calls() {
     EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
-    EXPR -w2 + w4 = 0
+    EXPR w2 = w4
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w7]
     EXPR w2*w7 - 1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w8, w9]
@@ -248,7 +248,7 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
-    EXPR -w2 + w4 = 0
+    EXPR w2 = w4
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
@@ -382,7 +382,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
-    EXPR -w2 + w4 = 0
+    EXPR w2 = w4
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
@@ -410,7 +410,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     EXPR w3*w4 + w5 - 1 = 0
     EXPR w3*w5 = 0
     EXPR w5 = 0
-    EXPR -w0 + w2 = 0
+    EXPR w0 = w2
 
     unconstrained func 0
      0: @2 = const u32 1
diff --git a/compiler/noirc_evaluator/src/acir/tests/call.rs b/compiler/noirc_evaluator/src/acir/tests/call.rs
index 5eca1363d05..b7b7fff5a2d 100644
--- a/compiler/noirc_evaluator/src/acir/tests/call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/call.rs
@@ -64,15 +64,15 @@ fn basic_call_with_outputs_assert(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR w2 - w3 = 0
+    EXPR w2 = w3
 
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 - w1 = 0
-    EXPR -w0 + w2 = 0
+    EXPR w0 = w1
+    EXPR w0 = w2
     ");
 }
 
@@ -107,15 +107,15 @@ fn call_output_as_next_call_input(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w2, w1], outputs: [w3]
-    EXPR w2 - w3 = 0
+    EXPR w2 = w3
 
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 - w1 = 0
-    EXPR -w0 + w2 = 0
+    EXPR w0 = w1
+    EXPR w0 = w2
     ");
 }
 
@@ -154,7 +154,7 @@ fn basic_nested_call(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR w2 - w3 = 0
+    EXPR w2 = w3
 
     func 1
     current witness: w4
@@ -164,14 +164,14 @@ fn basic_nested_call(inline_type: InlineType) {
     EXPR w0 - w3 + 2 = 0
     CALL func 2: PREDICATE: EXPR [ 1 ]
     inputs: [w3, w1], outputs: [w4]
-    EXPR w2 - w4 = 0
+    EXPR w2 = w4
 
     func 2
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 - w1 = 0
-    EXPR -w0 + w2 = 0
+    EXPR w0 = w1
+    EXPR w0 = w2
     ");
 }

From 25cdb7574ffb4e31735f5d3637a6f9fd01bed9bc Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 13:28:01 -0300
Subject: [PATCH 10/25] One more tiny change

---
 acvm-repo/acir/src/parser/tests.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index cd2d57f70ef..88dcd54dd23 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -742,7 +742,7 @@ fn fold_basic_mismatched_ids() {
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
-    EXPR -w0 + w2 = 0
+    EXPR w0 = w2
     ";
     let result = Program::from_str(src).err().unwrap();
     let ParserError::UnexpectedFunctionId { expected, found, .. } = result.get_error() else {

From 62c1e33c092675affdc11e739ed8775b64162888 Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 14:05:43 -0300
Subject: [PATCH 11/25] Don't print zero coefficients

---
 .../acir/src/native_types/expression/mod.rs   |  7 +-
 acvm-repo/acir/src/parser/mod.rs              |  8 +--
 acvm-repo/acir/src/parser/tests.rs            | 64 +++++++++----------
 .../compiler/optimizers/redundant_range.rs    |  6 +-
 .../noirc_evaluator/src/acir/tests/arrays.rs  | 24 +++----
 .../src/acir/tests/brillig_call.rs            | 46 ++++++-------
 6 files changed, 77 insertions(+), 78 deletions(-)

diff --git a/acvm-repo/acir/src/native_types/expression/mod.rs b/acvm-repo/acir/src/native_types/expression/mod.rs
index bcbc1aeaced..f3b0d999c6f 100644
--- a/acvm-repo/acir/src/native_types/expression/mod.rs
+++ b/acvm-repo/acir/src/native_types/expression/mod.rs
@@ -58,9 +58,12 @@ impl<F: std::fmt::Display> std::fmt::Display for Expression<F> {
         for i in &self.linear_combinations {
             write!(f, "({}, {}) ", i.0, i.1)?;
         }
-        write!(f, "{}", self.q_c)?;
 
-        write!(f, " ]")
+        let q_c_as_string = self.q_c.to_string();
+        if q_c_as_string != "0" {
+            write!(f, "{} ", self.q_c)?;
+        }
+        write!(f, "]")
     }
 }
 
diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index 42610582398..78645d3c72f 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -404,9 +404,8 @@ impl<'a> Parser<'a> {
             }
         }
 
-        let Some(q_c) = constant else {
-            return Err(ParserError::MissingConstantTerm { span: self.token.span() });
-        };
+        // If a constant isn't provided, we default it to zero
+        let q_c = constant.unwrap_or_default();
 
         Ok(Expression { mul_terms, linear_combinations, q_c })
     }
@@ -1114,8 +1113,6 @@ pub(crate) enum ParserError {
     ExpectedZero { found: Token, span: Span },
     #[error("Duplicate constant term in native Expression")]
     DuplicatedConstantTerm { found: Token, span: Span },
-    #[error("Missing constant term in native Expression")]
-    MissingConstantTerm { span: Span },
     #[error("Expected valid black box function name, found '{found}'")]
     ExpectedBlackBoxFuncName { found: Token, span: Span },
     #[error("Number does not fit in u32, got: '{number}'")]
@@ -1142,7 +1139,6 @@ impl ParserError {
             | ExpectedWitness { span, .. }
             | ExpectedZero { span, .. }
             | DuplicatedConstantTerm { span, .. }
-            | MissingConstantTerm { span }
             | ExpectedBlackBoxFuncName { span, .. }
             | IntegerLargerThanU32 { span, .. }
             | IncorrectInputLength { span, .. }
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 88dcd54dd23..556294cca7a 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -463,7 +463,7 @@ fn memory_read() {
     private parameters: []
     public parameters: []
     return values: []
-    MEM (id: 0, read at: EXPR [ (1, w0) 0 ], value: EXPR [ (1, w1) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w0) ], value: EXPR [ (1, w1) ])
     ";
     assert_circuit_roundtrip(src);
 }
@@ -475,7 +475,7 @@ fn memory_write() {
     private parameters: []
     public parameters: []
     return values: []
-    MEM (id: 3, write EXPR [ (1, w0) 0 ] at: EXPR [ (1, w1) 0 ])
+    MEM (id: 3, write EXPR [ (1, w0) ] at: EXPR [ (1, w1) ])
     ";
     assert_circuit_roundtrip(src);
 }
@@ -524,7 +524,7 @@ fn brillig_call() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
     EXPR w0 = w2
     ";
@@ -539,7 +539,7 @@ fn brillig_call_with_predicate() {
     public parameters: []
     return values: []
     BRILLIG CALL func 0: PREDICATE: EXPR [ 1 ]
-    inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
+    inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
     EXPR w0 = w2
     ";
@@ -612,27 +612,27 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w20]:32 bits []
     EXPR w20 - w21 - 5 = 0
     EXPR w21 - w22 - 3 = 0
-    MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w23) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w21) ], value: EXPR [ (1, w23) ])
     EXPR w23 = 111
-    MEM (id: 0, read at: EXPR [ (1, w22) 0 ], value: EXPR [ (1, w24) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w22) ], value: EXPR [ (1, w24) ])
     EXPR w24 = 101
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w22) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w25, w26]
     BLACKBOX::RANGE [w26]:32 bits []
     EXPR w22 - 4294967296*w25 - w26 + 4294967291 = 0
     EXPR w25 = 0
     EXPR w27 = 0
-    MEM (id: 0, write EXPR [ (1, w27) 0 ] at: EXPR [ (1, w22) 0 ])
-    MEM (id: 0, read at: EXPR [ (1, w21) 0 ], value: EXPR [ (1, w28) 0 ])
+    MEM (id: 0, write EXPR [ (1, w27) ] at: EXPR [ (1, w22) ])
+    MEM (id: 0, read at: EXPR [ (1, w21) ], value: EXPR [ (1, w28) ])
     EXPR w28 = 111
     EXPR w29 = 1
-    MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w30) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w29) ], value: EXPR [ (1, w30) ])
     EXPR w30 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967286 ], EXPR [ 4294967296 ]], outputs: [w31, w32]
     BLACKBOX::RANGE [w31]:1 bits []
     BLACKBOX::RANGE [w32]:32 bits []
     EXPR w21 - 4294967296*w31 - w32 + 4294967286 = 0
     EXPR -w21*w31 + w21 - w33 = 0
-    MEM (id: 0, read at: EXPR [ (1, w33) 0 ], value: EXPR [ (1, w34) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w33) ], value: EXPR [ (1, w34) ])
     EXPR -w31*w34 + 2*w31 + w34 - w35 - 2 = 0
     BLACKBOX::RANGE [w35]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w36, w37]
@@ -641,26 +641,26 @@ fn array_dynamic() {
     EXPR w21 - 4294967296*w36 - w37 + 4294967291 = 0
     EXPR w31*w36 - w36 = 0
     EXPR -w21*w31 + w21 - w38 = 0
-    MEM (id: 0, read at: EXPR [ (1, w38) 0 ], value: EXPR [ (1, w39) 0 ])
-    MEM (id: 0, read at: EXPR [ (1, w27) 0 ], value: EXPR [ (1, w40) 0 ])
-    MEM (id: 0, read at: EXPR [ (1, w29) 0 ], value: EXPR [ (1, w41) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w38) ], value: EXPR [ (1, w39) ])
+    MEM (id: 0, read at: EXPR [ (1, w27) ], value: EXPR [ (1, w40) ])
+    MEM (id: 0, read at: EXPR [ (1, w29) ], value: EXPR [ (1, w41) ])
     EXPR w42 = 2
-    MEM (id: 0, read at: EXPR [ (1, w42) 0 ], value: EXPR [ (1, w43) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w42) ], value: EXPR [ (1, w43) ])
     EXPR w44 = 3
-    MEM (id: 0, read at: EXPR [ (1, w44) 0 ], value: EXPR [ (1, w45) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w44) ], value: EXPR [ (1, w45) ])
     EXPR w46 = 0
-    MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w47) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w47) ])
     INIT (id: 3, len: 5, witnesses: [w40, w41, w43, w45, w47])
     EXPR -w31*w35 + w31*w39 + w35 - w48 = 0
-    MEM (id: 3, write EXPR [ (1, w48) 0 ] at: EXPR [ (1, w38) 0 ])
-    MEM (id: 3, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w49) 0 ])
-    MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w50) 0 ])
+    MEM (id: 3, write EXPR [ (1, w48) ] at: EXPR [ (1, w38) ])
+    MEM (id: 3, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w49) ])
+    MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w50) ])
     EXPR -w31*w36 = 0
     EXPR w21*w31 - w51 = 0
-    MEM (id: 0, read at: EXPR [ (1, w51) 0 ], value: EXPR [ (1, w52) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w51) ], value: EXPR [ (1, w52) ])
     EXPR -w31*w52 + w52 - w53 = 0
-    MEM (id: 0, write EXPR [ (1, w53) 0 ] at: EXPR [ (1, w51) 0 ])
-    MEM (id: 0, read at: EXPR [ (1, w46) 0 ], value: EXPR [ (1, w54) 0 ])
+    MEM (id: 0, write EXPR [ (1, w53) ] at: EXPR [ (1, w51) ])
+    MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w54) ])
     EXPR -w31 - w55 + 1 = 0
     EXPR -w31*w49 + w31*w50 + w49 - w56 = 0
     EXPR w31*w54 + w55*w56 - 109 = 0
@@ -670,14 +670,14 @@ fn array_dynamic() {
     EXPR w60 = 176
     EXPR w61 = 8
     INIT (id: 4, len: 5, witnesses: [w57, w58, w59, w60, w61])
-    MEM (id: 4, read at: EXPR [ (1, w7) 0 ], value: EXPR [ (1, w62) 0 ])
-    MEM (id: 4, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w63) 0 ])
-    MEM (id: 4, read at: EXPR [ (1, w9) 0 ], value: EXPR [ (1, w64) 0 ])
-    MEM (id: 4, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w65) 0 ])
-    MEM (id: 4, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w66) 0 ])
-    BRILLIG CALL func 1: inputs: [EXPR [ (1, w62) (1, w63) (1, w64) (1, w65) (1, w66) 0 ]], outputs: [w67]
+    MEM (id: 4, read at: EXPR [ (1, w7) ], value: EXPR [ (1, w62) ])
+    MEM (id: 4, read at: EXPR [ (1, w8) ], value: EXPR [ (1, w63) ])
+    MEM (id: 4, read at: EXPR [ (1, w9) ], value: EXPR [ (1, w64) ])
+    MEM (id: 4, read at: EXPR [ (1, w10) ], value: EXPR [ (1, w65) ])
+    MEM (id: 4, read at: EXPR [ (1, w11) ], value: EXPR [ (1, w66) ])
+    BRILLIG CALL func 1: inputs: [EXPR [ (1, w62) (1, w63) (1, w64) (1, w65) (1, w66) ]], outputs: [w67]
     EXPR w62*w67 + w63*w67 + w64*w67 + w65*w67 + w66*w67 - 1 = 0
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w18) 0 ], EXPR [ 4294967296 ]], outputs: [w68, w69]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w18) ], EXPR [ 4294967296 ]], outputs: [w68, w69]
     BLACKBOX::RANGE [w68]:222 bits []
     BLACKBOX::RANGE [w69]:32 bits []
     EXPR w18 - 4294967296*w68 - w69 = 0
@@ -695,7 +695,7 @@ fn array_dynamic() {
     EXPR -w17*w74 + w17 - 3*w74 - w76 + 3 = 0
     BLACKBOX::RANGE [w76]:32 bits []
     EXPR -w74*w76 + w76 - w77 = 0
-    MEM (id: 1, read at: EXPR [ (1, w77) 0 ], value: EXPR [ (1, w78) 0 ])
+    MEM (id: 1, read at: EXPR [ (1, w77) ], value: EXPR [ (1, w78) ])
     EXPR w15*w74 - w74*w78 - w15 + w78 = 0
     ";
     assert_circuit_roundtrip(src);
@@ -717,7 +717,7 @@ fn fold_basic() {
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
     EXPR w0 = w2
     ";
@@ -740,7 +740,7 @@ fn fold_basic_mismatched_ids() {
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) 0 ]], outputs: [w3]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
     EXPR w0 = w2
     ";
diff --git a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
index 77126b0f5f9..b18582a89c4 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
@@ -441,9 +441,9 @@ mod tests {
         public parameters: []
         return values: []
         BLACKBOX::RANGE [w1]:32 bits []
-        BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: []
+        BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) ]], outputs: []
         BLACKBOX::RANGE [w1]:16 bits []
-        BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: []
+        BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) ]], outputs: []
         EXPR w1 = 0
         ");
 
@@ -478,7 +478,7 @@ mod tests {
         public parameters: []
         return values: []
         INIT (id: 0, len: 8, witnesses: [w0, w0, w0, w0, w0, w0, w0, w0])
-        MEM (id: 0, read at: EXPR [ (1, w1) 0 ], value: EXPR [ (1, w2) 0 ])
+        MEM (id: 0, read at: EXPR [ (1, w1) ], value: EXPR [ (1, w2) ])
         ");
     }
 }
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index 7579c054716..9d2276eabed 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -53,7 +53,7 @@ fn constant_array_access_out_of_bounds() {
     EXPR w1 = 1
     INIT (id: 0, len: 2, witnesses: [w0, w1])
     EXPR w2 = 5
-    MEM (id: 0, read at: EXPR [ (1, w2) 0 ], value: EXPR [ (1, w3) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w2) ], value: EXPR [ (1, w3) ])
     EXPR w3 = 0
     ");
 }
@@ -96,7 +96,7 @@ fn generates_memory_op_for_dynamic_read() {
     public parameters: []
     return values: []
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
-    MEM (id: 0, read at: EXPR [ (1, w3) 0 ], value: EXPR [ (1, w4) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w3) ], value: EXPR [ (1, w4) ])
     EXPR w4 = 10
     ");
 }
@@ -121,13 +121,13 @@ fn generates_memory_op_for_dynamic_write() {
     return values: [w4, w5, w6]
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
     EXPR w7 = 10
-    MEM (id: 1, write EXPR [ (1, w7) 0 ] at: EXPR [ (1, w3) 0 ])
+    MEM (id: 1, write EXPR [ (1, w7) ] at: EXPR [ (1, w3) ])
     EXPR w8 = 0
-    MEM (id: 1, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ])
+    MEM (id: 1, read at: EXPR [ (1, w8) ], value: EXPR [ (1, w9) ])
     EXPR w10 = 1
-    MEM (id: 1, read at: EXPR [ (1, w10) 0 ], value: EXPR [ (1, w11) 0 ])
+    MEM (id: 1, read at: EXPR [ (1, w10) ], value: EXPR [ (1, w11) ])
     EXPR w12 = 2
-    MEM (id: 1, read at: EXPR [ (1, w12) 0 ], value: EXPR [ (1, w13) 0 ])
+    MEM (id: 1, read at: EXPR [ (1, w12) ], value: EXPR [ (1, w13) ])
     EXPR w4 = w9
     EXPR w5 = w11
     EXPR w6 = w13
@@ -162,7 +162,7 @@ fn generates_predicated_index_for_dynamic_read() {
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
     EXPR w3*w4 - w5 = 0
-    MEM (id: 0, read at: EXPR [ (1, w5) 0 ], value: EXPR [ (1, w6) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w5) ], value: EXPR [ (1, w6) ])
     EXPR w6 = 10
     ");
 }
@@ -200,16 +200,16 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
     EXPR w3*w4 - w8 = 0
-    MEM (id: 0, read at: EXPR [ (1, w8) 0 ], value: EXPR [ (1, w9) 0 ])
+    MEM (id: 0, read at: EXPR [ (1, w8) ], value: EXPR [ (1, w9) ])
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
     EXPR -w4*w9 + 10*w4 + w9 - w10 = 0
-    MEM (id: 1, write EXPR [ (1, w10) 0 ] at: EXPR [ (1, w8) 0 ])
+    MEM (id: 1, write EXPR [ (1, w10) ] at: EXPR [ (1, w8) ])
     EXPR w11 = 0
-    MEM (id: 1, read at: EXPR [ (1, w11) 0 ], value: EXPR [ (1, w12) 0 ])
+    MEM (id: 1, read at: EXPR [ (1, w11) ], value: EXPR [ (1, w12) ])
     EXPR w13 = 1
-    MEM (id: 1, read at: EXPR [ (1, w13) 0 ], value: EXPR [ (1, w14) 0 ])
+    MEM (id: 1, read at: EXPR [ (1, w13) ], value: EXPR [ (1, w14) ])
     EXPR w15 = 2
-    MEM (id: 1, read at: EXPR [ (1, w15) 0 ], value: EXPR [ (1, w16) 0 ])
+    MEM (id: 1, read at: EXPR [ (1, w15) ], value: EXPR [ (1, w16) ])
     EXPR w5 = w12
     EXPR w6 = w14
     EXPR w7 = w16
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index a468340ea07..cac103cfb96 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -45,12 +45,12 @@ fn multiple_brillig_calls_one_bytecode() {
     private parameters: [w0, w1]
     public parameters: []
     return values: []
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w2]
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w3]
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4]
-    BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w5]
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w6]
-    BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w2]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w3]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4]
+    BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w5]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w6]
+    BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w7]
 
     unconstrained func 0
      0: @2 = const u32 1
@@ -152,18 +152,18 @@ fn multiple_brillig_stdlib_calls() {
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
     EXPR w1*w3 - 1 = 0
-    BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
+    BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
     EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
     EXPR w2 = w4
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w7]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) ]], outputs: [w7]
     EXPR w2*w7 - 1 = 0
-    BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w8, w9]
+    BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w8, w9]
     BLACKBOX::RANGE [w9]:32 bits []
     EXPR w2 - w9 - w10 - 1 = 0
     BLACKBOX::RANGE [w10]:32 bits []
@@ -240,22 +240,22 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
-    BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
+    BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
     EXPR w1*w3 - 1 = 0
-    BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
+    BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
     EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
     EXPR w2 = w4
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w8]
     BLACKBOX::RANGE [w8]:32 bits []
-    BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w9]
+    BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) ]], outputs: [w9]
     EXPR w2*w9 - 1 = 0
-    BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w10, w11]
+    BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w10, w11]
     BLACKBOX::RANGE [w11]:32 bits []
     EXPR w2 - w11 - w12 - 1 = 0
     BLACKBOX::RANGE [w12]:32 bits []
@@ -374,24 +374,24 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
-    BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) 0 ]], outputs: [w3]
+    BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
     EXPR w1*w3 - 1 = 0
-    BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w4, w5]
+    BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
     EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
     EXPR w2 = w4
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w7]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
-    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) 0 ], EXPR [ (1, w1) 0 ]], outputs: [w8]
+    BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w8]
     BLACKBOX::RANGE [w8]:32 bits []
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w9]
-    BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) 0 ]], outputs: [w10]
+    BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) ]], outputs: [w10]
     EXPR w2*w10 - 1 = 0
-    BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) 0 ], EXPR [ (1, w2) 0 ]], outputs: [w11, w12]
+    BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w11, w12]
     BLACKBOX::RANGE [w12]:32 bits []
     EXPR w2 - w12 - w13 - 1 = 0
     BLACKBOX::RANGE [w13]:32 bits []
@@ -406,7 +406,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
     EXPR w0 - w1 - w3 = 0
-    BRILLIG CALL func 1: inputs: [EXPR [ (1, w3) 0 ]], outputs: [w4]
+    BRILLIG CALL func 1: inputs: [EXPR [ (1, w3) ]], outputs: [w4]
     EXPR w3*w4 + w5 - 1 = 0
     EXPR w3*w5 = 0
     EXPR w5 = 0

From 27fedc6ca2554a073fe17c4ee6e205b91daf93a0 Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 14:38:42 -0300
Subject: [PATCH 12/25] Try to show q_c on the right-hand side of the equation

---
 acvm-repo/acir/src/circuit/mod.rs             |  2 +-
 acvm-repo/acir/src/circuit/opcodes.rs         | 13 +++++---
 acvm-repo/acir/src/parser/mod.rs              | 16 ++++++----
 acvm-repo/acir/src/parser/tests.rs            | 32 +++++++++----------
 .../src/acir/tests/brillig_call.rs            | 26 +++++++--------
 .../noirc_evaluator/src/acir/tests/call.rs    |  2 +-
 6 files changed, 49 insertions(+), 42 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/mod.rs b/acvm-repo/acir/src/circuit/mod.rs
index 1dd1e2f8bb0..85056107edc 100644
--- a/acvm-repo/acir/src/circuit/mod.rs
+++ b/acvm-repo/acir/src/circuit/mod.rs
@@ -544,7 +544,7 @@ mod tests {
         private parameters: []
         public parameters: [w2]
         return values: [w2]
-        EXPR 2*w1 + 8 = 0
+        EXPR 2*w1 = -8
         BLACKBOX::RANGE [w1]:8 bits []
         BLACKBOX::AND [w1, w2]:4 bits [w3]
         BLACKBOX::KECCAKF1600 [w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25] [w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43, w44, w45, w46, w47, w48, w49, w50]
diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index c3513222e24..fe4d2ffaa28 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -246,9 +246,13 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                     printed_term = true;
                 }
 
-                if !expr.q_c.is_zero()
-                    || (expr.mul_terms.is_empty() && expr.linear_combinations.is_empty())
-                {
+                if printed_term {
+                    // Change `... + c = 0` to `... = -c`
+                    let q_c = -expr.q_c;
+                    write!(f, " = {q_c}")?;
+                } else if expr.q_c.is_zero() {
+                    write!(f, "0 = 0")?;
+                } else {
                     let coefficient = expr.q_c;
                     let coefficient_as_string = coefficient.to_string();
                     let coefficient_is_negative = coefficient_as_string.starts_with('-');
@@ -267,10 +271,9 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                         coefficient
                     };
                     write!(f, "{coefficient}")?;
+                    write!(f, " = 0")?;
                 }
 
-                write!(f, " = 0")?;
-
                 Ok(())
             }
             Opcode::BlackBoxFuncCall(g) => g.fmt(f),
diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index 78645d3c72f..0ed30431541 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -336,12 +336,19 @@ impl<'a> Parser<'a> {
             if self.eat(Token::Equal)? {
                 let zero_token = self.token.token().clone();
                 let span = self.token.span();
-                let Some(zero) = self.eat_field_element()? else {
+                let Some(q_c) = self.eat_field_element()? else {
                     return self.expected_field_element();
                 };
 
-                if !zero.is_zero() {
-                    return Err(ParserError::ExpectedZero { found: zero_token, span });
+                if !q_c.is_zero() {
+                    if constant.is_some() {
+                        return Err(ParserError::DuplicatedConstantTerm {
+                            found: zero_token,
+                            span,
+                        });
+                    }
+                    // If we have `... = q_c` we produce `... - q_c = 0`
+                    constant = Some(-q_c);
                 }
 
                 break;
@@ -1109,8 +1116,6 @@ pub(crate) enum ParserError {
     ExpectedFieldElement { found: Token, span: Span },
     #[error("Expected a witness index, found '{found}'")]
     ExpectedWitness { found: Token, span: Span },
-    #[error("Expected a zero, found '{found}'")]
-    ExpectedZero { found: Token, span: Span },
     #[error("Duplicate constant term in native Expression")]
     DuplicatedConstantTerm { found: Token, span: Span },
     #[error("Expected valid black box function name, found '{found}'")]
@@ -1137,7 +1142,6 @@ impl ParserError {
             | ExpectedIdentifier { span, .. }
             | ExpectedFieldElement { span, .. }
             | ExpectedWitness { span, .. }
-            | ExpectedZero { span, .. }
             | DuplicatedConstantTerm { span, .. }
             | ExpectedBlackBoxFuncName { span, .. }
             | IntegerLargerThanU32 { span, .. }
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 556294cca7a..9e31399f246 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -525,7 +525,7 @@ fn brillig_call() {
     public parameters: []
     return values: []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
-    EXPR w0*w3 - w1*w3 - 1 = 0
+    EXPR w0*w3 - w1*w3 = 1
     EXPR w0 = w2
     ";
     assert_circuit_roundtrip(src);
@@ -540,7 +540,7 @@ fn brillig_call_with_predicate() {
     return values: []
     BRILLIG CALL func 0: PREDICATE: EXPR [ 1 ]
     inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
-    EXPR w0*w3 - w1*w3 - 1 = 0
+    EXPR w0*w3 - w1*w3 = 1
     EXPR w0 = w2
     ";
     assert_circuit_roundtrip(src);
@@ -610,15 +610,15 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w19]:32 bits []
     EXPR w5 - w19 - w20 = 0
     BLACKBOX::RANGE [w20]:32 bits []
-    EXPR w20 - w21 - 5 = 0
-    EXPR w21 - w22 - 3 = 0
+    EXPR w20 - w21 = 5
+    EXPR w21 - w22 = 3
     MEM (id: 0, read at: EXPR [ (1, w21) ], value: EXPR [ (1, w23) ])
     EXPR w23 = 111
     MEM (id: 0, read at: EXPR [ (1, w22) ], value: EXPR [ (1, w24) ])
     EXPR w24 = 101
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w22) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w25, w26]
     BLACKBOX::RANGE [w26]:32 bits []
-    EXPR w22 - 4294967296*w25 - w26 + 4294967291 = 0
+    EXPR w22 - 4294967296*w25 - w26 = -4294967291
     EXPR w25 = 0
     EXPR w27 = 0
     MEM (id: 0, write EXPR [ (1, w27) ] at: EXPR [ (1, w22) ])
@@ -630,15 +630,15 @@ fn array_dynamic() {
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967286 ], EXPR [ 4294967296 ]], outputs: [w31, w32]
     BLACKBOX::RANGE [w31]:1 bits []
     BLACKBOX::RANGE [w32]:32 bits []
-    EXPR w21 - 4294967296*w31 - w32 + 4294967286 = 0
+    EXPR w21 - 4294967296*w31 - w32 = -4294967286
     EXPR -w21*w31 + w21 - w33 = 0
     MEM (id: 0, read at: EXPR [ (1, w33) ], value: EXPR [ (1, w34) ])
-    EXPR -w31*w34 + 2*w31 + w34 - w35 - 2 = 0
+    EXPR -w31*w34 + 2*w31 + w34 - w35 = 2
     BLACKBOX::RANGE [w35]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w36, w37]
     BLACKBOX::RANGE [w36]:1 bits []
     BLACKBOX::RANGE [w37]:32 bits []
-    EXPR w21 - 4294967296*w36 - w37 + 4294967291 = 0
+    EXPR w21 - 4294967296*w36 - w37 = -4294967291
     EXPR w31*w36 - w36 = 0
     EXPR -w21*w31 + w21 - w38 = 0
     MEM (id: 0, read at: EXPR [ (1, w38) ], value: EXPR [ (1, w39) ])
@@ -661,9 +661,9 @@ fn array_dynamic() {
     EXPR -w31*w52 + w52 - w53 = 0
     MEM (id: 0, write EXPR [ (1, w53) ] at: EXPR [ (1, w51) ])
     MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w54) ])
-    EXPR -w31 - w55 + 1 = 0
+    EXPR -w31 - w55 = -1
     EXPR -w31*w49 + w31*w50 + w49 - w56 = 0
-    EXPR w31*w54 + w55*w56 - 109 = 0
+    EXPR w31*w54 + w55*w56 = 109
     EXPR w57 = 246
     EXPR w58 = 159
     EXPR w59 = 32
@@ -676,23 +676,23 @@ fn array_dynamic() {
     MEM (id: 4, read at: EXPR [ (1, w10) ], value: EXPR [ (1, w65) ])
     MEM (id: 4, read at: EXPR [ (1, w11) ], value: EXPR [ (1, w66) ])
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w62) (1, w63) (1, w64) (1, w65) (1, w66) ]], outputs: [w67]
-    EXPR w62*w67 + w63*w67 + w64*w67 + w65*w67 + w66*w67 - 1 = 0
+    EXPR w62*w67 + w63*w67 + w64*w67 + w65*w67 + w66*w67 = 1
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w18) ], EXPR [ 4294967296 ]], outputs: [w68, w69]
     BLACKBOX::RANGE [w68]:222 bits []
     BLACKBOX::RANGE [w69]:32 bits []
     EXPR w18 - 4294967296*w68 - w69 = 0
-    EXPR -w68 - w70 + 5096253676302562286669017222071363378443840053029366383258766538131 = 0
+    EXPR -w68 - w70 = -5096253676302562286669017222071363378443840053029366383258766538131
     BLACKBOX::RANGE [w70]:222 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (-1, w68) 5096253676302562286669017222071363378443840053029366383258766538131 ]], outputs: [w71]
-    EXPR -w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + w72 - 1 = 0
+    EXPR -w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + w72 = 1
     EXPR -w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72 = 0
     EXPR w69*w72 + 268435455*w72 - w73 = 0
     BLACKBOX::RANGE [w73]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (-1, w69) 4294967299 ], EXPR [ 4294967296 ]], outputs: [w74, w75]
     BLACKBOX::RANGE [w74]:1 bits []
     BLACKBOX::RANGE [w75]:32 bits []
-    EXPR -w69 - 4294967296*w74 - w75 + 4294967299 = 0
-    EXPR -w17*w74 + w17 - 3*w74 - w76 + 3 = 0
+    EXPR -w69 - 4294967296*w74 - w75 = -4294967299
+    EXPR -w17*w74 + w17 - 3*w74 - w76 = -3
     BLACKBOX::RANGE [w76]:32 bits []
     EXPR -w74*w76 + w76 - w77 = 0
     MEM (id: 1, read at: EXPR [ (1, w77) ], value: EXPR [ (1, w78) ])
@@ -718,7 +718,7 @@ fn fold_basic() {
     public parameters: []
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
-    EXPR w0*w3 - w1*w3 - 1 = 0
+    EXPR w0*w3 - w1*w3 = 1
     EXPR w0 = w2
     ";
     assert_program_roundtrip(src);
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index cac103cfb96..049cfef5c26 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -153,19 +153,19 @@ fn multiple_brillig_stdlib_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
-    EXPR w1*w3 - 1 = 0
+    EXPR w1*w3 = 1
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 - w5 - w6 - 1 = 0
+    EXPR w1 - w5 - w6 = 1
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
     EXPR w2 = w4
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) ]], outputs: [w7]
-    EXPR w2*w7 - 1 = 0
+    EXPR w2*w7 = 1
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w8, w9]
     BLACKBOX::RANGE [w9]:32 bits []
-    EXPR w2 - w9 - w10 - 1 = 0
+    EXPR w2 - w9 - w10 = 1
     BLACKBOX::RANGE [w10]:32 bits []
     EXPR -w2*w8 + w1 - w9 = 0
     EXPR w8 = 1
@@ -241,11 +241,11 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
-    EXPR w1*w3 - 1 = 0
+    EXPR w1*w3 = 1
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 - w5 - w6 - 1 = 0
+    EXPR w1 - w5 - w6 = 1
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
     EXPR w2 = w4
@@ -254,10 +254,10 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w8]
     BLACKBOX::RANGE [w8]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) ]], outputs: [w9]
-    EXPR w2*w9 - 1 = 0
+    EXPR w2*w9 = 1
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w10, w11]
     BLACKBOX::RANGE [w11]:32 bits []
-    EXPR w2 - w11 - w12 - 1 = 0
+    EXPR w2 - w11 - w12 = 1
     BLACKBOX::RANGE [w12]:32 bits []
     EXPR -w2*w10 + w1 - w11 = 0
     EXPR w10 = 1
@@ -375,11 +375,11 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
-    EXPR w1*w3 - 1 = 0
+    EXPR w1*w3 = 1
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 - w5 - w6 - 1 = 0
+    EXPR w1 - w5 - w6 = 1
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
     EXPR w2 = w4
@@ -390,10 +390,10 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w9]
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) ]], outputs: [w10]
-    EXPR w2*w10 - 1 = 0
+    EXPR w2*w10 = 1
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w11, w12]
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR w2 - w12 - w13 - 1 = 0
+    EXPR w2 - w12 - w13 = 1
     BLACKBOX::RANGE [w13]:32 bits []
     EXPR -w2*w11 + w1 - w12 = 0
     EXPR w11 = 1
@@ -407,7 +407,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     EXPR w0 - w1 - w3 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w3) ]], outputs: [w4]
-    EXPR w3*w4 + w5 - 1 = 0
+    EXPR w3*w4 + w5 = 1
     EXPR w3*w5 = 0
     EXPR w5 = 0
     EXPR w0 = w2
diff --git a/compiler/noirc_evaluator/src/acir/tests/call.rs b/compiler/noirc_evaluator/src/acir/tests/call.rs
index b7b7fff5a2d..a9b59ff6478 100644
--- a/compiler/noirc_evaluator/src/acir/tests/call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/call.rs
@@ -161,7 +161,7 @@ fn basic_nested_call(inline_type: InlineType) {
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 - w3 + 2 = 0
+    EXPR w0 - w3 = -2
     CALL func 2: PREDICATE: EXPR [ 1 ]
     inputs: [w3, w1], outputs: [w4]
     EXPR w2 = w4

From fb83a4aa99abc6c936bf24c947d922fa8387509e Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 15:07:03 -0300
Subject: [PATCH 13/25] Use new syntax in comments

---
 compiler/noirc_evaluator/src/acir/tests/arrays.rs | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index 9d2276eabed..0b75317345f 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -149,7 +149,7 @@ fn generates_predicated_index_for_dynamic_read() {
 
     // w0, w1, w2 represents the array
     // So w3 represents our index and w4 is our predicate
-    // We can see that before the read we have `EXPR [ (1, w3, w4) (-1, w5) 0 ]`
+    // We can see that before the read we have `w3*w4 - w5 = 0`
     // As the index is zero this is a simplified version of `index*predicate + (1-predicate)*offset`
     // w5 is then used as the index which we use to read from the memory block
     assert_circuit_snapshot!(program, @r"
@@ -180,15 +180,15 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     let program = ssa_to_acir_program(src);
 
     // Similar to the `generates_predicated_index_for_dynamic_read` test we can
-    // see how `EXPR [ (1, w3, w4) (-1, w8) 0 ]` forms our predicated index.
+    // see how `w3*w4 - w8 = 0` forms our predicated index.
     // However, now we also have extra logic for generating a dummy value.
     // The original value we want to write is `Field 10` and our predicate is `w4`.
     // We read the value at the predicated index into `w9`. This is our dummy value.
     // We can then see how we form our new store value with:
-    // `EXPR [ (-1, w4, w9) (10, w4) (1, w9) (-1, w10) 0 ]` -> (predicate*value + (1-predicate)*dummy)
-    // `(10, w4)` -> predicate*value
-    // `(-1, w4, w9)` -> (-predicate * dummy)
-    // `(1, w9)` -> dummy
+    // `EXPR -w4*w9 + 10*w4 + w9 - w10 = 0` -> (predicate*value + (1-predicate)*dummy)
+    // `10*w4` -> predicate*value
+    // `-w4*w9` -> (-predicate * dummy)
+    // `w9` -> dummy
     // As expected, we then store `w10` at the predicated index `w8`.
     assert_circuit_snapshot!(program, @r"
     func 0

From 32304155a72b46552436a587b1ee72dc12d7f589 Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Tue, 23 Sep 2025 16:50:22 -0300
Subject: [PATCH 14/25] Update acvm-repo/acir/src/circuit/opcodes.rs

---
 acvm-repo/acir/src/circuit/opcodes.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index fe4d2ffaa28..c53ec06e9d2 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -169,7 +169,7 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                     }
                 }
 
-                // Chec if it's `-wN * wM = 0` or `wN * -wM = 0` in which case we can
+                // Check if it's `-wN * wM = 0` or `wN * -wM = 0` in which case we can
                 // print it as `wN = wM`.
                 if expr.mul_terms.is_empty()
                     && expr.linear_combinations.len() == 2

From accc53da0b5c93799c3dab094084e1d2ade31018 Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Wed, 24 Sep 2025 09:36:49 -0300
Subject: [PATCH 15/25] Simpler and better parsing

---
 acvm-repo/acir/src/parser/mod.rs | 159 ++++++++++++++++---------------
 1 file changed, 83 insertions(+), 76 deletions(-)

diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index 0ed30431541..b83bfbb3858 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -261,67 +261,44 @@ impl<'a> Parser<'a> {
     }
 
     fn parse_assert_zero_expression(&mut self) -> ParseResult<Expression<FieldElement>> {
+        // 'EXPR'
         self.eat_keyword_or_error(Keyword::Expression)?;
 
-        let mut linear_combinations = Vec::new();
-        let mut mul_terms = Vec::new();
-        let mut constant: Option<FieldElement> = None;
-        let mut first = true;
-        let mut negative = self.eat(Token::Minus)?;
+        // Parse the left-hand side terms
+        let lhs_terms = self.parse_terms_or_error()?;
 
-        loop {
-            if let Some(w1) = self.eat_witness()? {
-                let coefficient = FieldElement::one();
-                let coefficient = if negative { -coefficient } else { coefficient };
-
-                if first && self.eat(Token::Equal)? {
-                    if let Some(w2) = self.eat_witness()? {
-                        // Here we parsed `coefficient*w1 = w2` so we produce `coefficient*w1 - w2 = 0`
-                        linear_combinations.push((coefficient, w1));
-                        linear_combinations.push((-FieldElement::one(), w2));
-                        break;
-                    }
+        // '='
+        self.eat_or_error(Token::Equal)?;
 
-                    let q_c = self.eat_field_or_error()?;
+        // Parse the right-hand side terms
+        let rhs_terms = self.parse_terms_or_error()?;
 
-                    // Here we parsed `coefficient*w1 = constant` so we produce `coefficient*w1 - q_c = 0`
-                    linear_combinations.push((coefficient, w1));
-                    constant = Some(-q_c);
-                    break;
-                }
+        // "Move" the terms to the left by negating them
+        let rhs_terms = rhs_terms.into_iter().map(|term| term.negate()).collect::<Vec<_>>();
 
-                if self.eat(Token::Star)? {
-                    let w2 = self.eat_witness_or_error()?;
-                    mul_terms.push((coefficient, w1, w2));
-                } else {
-                    linear_combinations.push((coefficient, w1));
-                }
-            } else if let Some(coefficient) = self.eat_field_element()? {
-                let coefficient = if negative { -coefficient } else { coefficient };
-
-                if self.eat(Token::Star)? {
-                    let w1 = self.eat_witness_or_error()?;
+        // Gather all terms, summing the constants
+        let mut q_c = FieldElement::zero();
+        let mut linear_combinations = Vec::new();
+        let mut mul_terms = Vec::new();
 
-                    if self.eat(Token::Star)? {
-                        let w2 = self.eat_witness_or_error()?;
-                        mul_terms.push((coefficient, w1, w2));
-                    } else {
-                        linear_combinations.push((coefficient, w1));
-                    }
-                } else {
-                    if constant.is_some() {
-                        return Err(ParserError::DuplicatedConstantTerm {
-                            found: self.token.token().clone(),
-                            span: self.token.span(),
-                        });
-                    }
-                    constant = Some(coefficient);
-                }
-            } else {
-                return self.expected_field_element();
+        for term in lhs_terms.into_iter().chain(rhs_terms) {
+            match term {
+                Term::Constant(c) => q_c += c,
+                Term::Linear(c, w) => linear_combinations.push((c, w)),
+                Term::Multiplication(c, w1, w2) => mul_terms.push((c, w1, w2)),
             }
+        }
 
-            first = false;
+        Ok(Expression { mul_terms, linear_combinations, q_c })
+    }
+
+    fn parse_terms_or_error(&mut self) -> ParseResult<Vec<Term>> {
+        let mut terms = Vec::new();
+        let mut negative = self.eat(Token::Minus)?;
+        loop {
+            let term = self.parse_term_or_error()?;
+            let term = if negative { term.negate() } else { term };
+            terms.push(term);
 
             if self.eat(Token::Plus)? {
                 negative = false;
@@ -333,34 +310,37 @@ impl<'a> Parser<'a> {
                 continue;
             }
 
-            if self.eat(Token::Equal)? {
-                let zero_token = self.token.token().clone();
-                let span = self.token.span();
-                let Some(q_c) = self.eat_field_element()? else {
-                    return self.expected_field_element();
-                };
-
-                if !q_c.is_zero() {
-                    if constant.is_some() {
-                        return Err(ParserError::DuplicatedConstantTerm {
-                            found: zero_token,
-                            span,
-                        });
-                    }
-                    // If we have `... = q_c` we produce `... - q_c = 0`
-                    constant = Some(-q_c);
-                }
+            break;
+        }
+        Ok(terms)
+    }
 
-                break;
+    fn parse_term_or_error(&mut self) -> ParseResult<Term> {
+        if let Some(coefficient) = self.eat_field_element()? {
+            if self.eat(Token::Star)? {
+                let w1 = self.eat_witness_or_error()?;
+                self.parse_linear_or_multiplication_term(coefficient, w1)
+            } else {
+                Ok(Term::Constant(coefficient))
             }
-
-            return self.expected_token(Token::Equal);
+        } else if let Some(w1) = self.eat_witness()? {
+            self.parse_linear_or_multiplication_term(FieldElement::one(), w1)
+        } else {
+            self.expected_term()
         }
+    }
 
-        // If a constant isn't provided, we default it to zero
-        let q_c = constant.unwrap_or_default();
-
-        Ok(Expression { mul_terms, linear_combinations, q_c })
+    fn parse_linear_or_multiplication_term(
+        &mut self,
+        coefficient: FieldElement,
+        w1: Witness,
+    ) -> Result<Term, ParserError> {
+        if self.eat(Token::Star)? {
+            let w2 = self.eat_witness_or_error()?;
+            Ok(Term::Multiplication(coefficient, w1, w2))
+        } else {
+            Ok(Term::Linear(coefficient, w1))
+        }
     }
 
     fn parse_arithmetic_expression(&mut self) -> ParseResult<Expression<FieldElement>> {
@@ -1079,6 +1059,13 @@ impl<'a> Parser<'a> {
         })
     }
 
+    fn expected_term<T>(&mut self) -> ParseResult<T> {
+        Err(ParserError::ExpectedTerm {
+            found: self.token.token().clone(),
+            span: self.token.span(),
+        })
+    }
+
     fn expected_token<T>(&mut self, token: Token) -> ParseResult<T> {
         Err(ParserError::ExpectedToken {
             token,
@@ -1100,6 +1087,23 @@ fn eof_spanned_token() -> SpannedToken {
     SpannedToken::new(Token::Eof, Default::default())
 }
 
+#[derive(Debug, Clone, Copy)]
+enum Term {
+    Constant(FieldElement),
+    Linear(FieldElement, Witness),
+    Multiplication(FieldElement, Witness, Witness),
+}
+
+impl Term {
+    fn negate(self) -> Self {
+        match self {
+            Term::Constant(c) => Term::Constant(-c),
+            Term::Linear(c, w) => Term::Linear(-c, w),
+            Term::Multiplication(c, w1, w2) => Term::Multiplication(-c, w1, w2),
+        }
+    }
+}
+
 type ParseResult<T> = Result<T, ParserError>;
 
 #[derive(Debug, Error)]
@@ -1116,6 +1120,8 @@ pub(crate) enum ParserError {
     ExpectedFieldElement { found: Token, span: Span },
     #[error("Expected a witness index, found '{found}'")]
     ExpectedWitness { found: Token, span: Span },
+    #[error("Expected a term, found '{found}'")]
+    ExpectedTerm { found: Token, span: Span },
     #[error("Duplicate constant term in native Expression")]
     DuplicatedConstantTerm { found: Token, span: Span },
     #[error("Expected valid black box function name, found '{found}'")]
@@ -1142,6 +1148,7 @@ impl ParserError {
             | ExpectedIdentifier { span, .. }
             | ExpectedFieldElement { span, .. }
             | ExpectedWitness { span, .. }
+            | ExpectedTerm { span, .. }
             | DuplicatedConstantTerm { span, .. }
             | ExpectedBlackBoxFuncName { span, .. }
             | IntegerLargerThanU32 { span, .. }

From b22518eb28f750588bf1bda812b7328f01c489f6 Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Wed, 24 Sep 2025 09:52:49 -0300
Subject: [PATCH 16/25] One more special case

---
 acvm-repo/acir/src/circuit/opcodes.rs         | 33 ++++++++++++++++---
 acvm-repo/acir/src/parser/tests.rs            | 31 ++++++++++++++---
 .../compiler/optimizers/merge_expressions.rs  |  2 +-
 .../noirc_evaluator/src/acir/tests/arrays.rs  |  4 +--
 .../noirc_evaluator/src/acir/tests/mod.rs     |  2 +-
 5 files changed, 59 insertions(+), 13 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index c53ec06e9d2..90b6f3a1e51 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -149,8 +149,8 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
             Opcode::AssertZero(expr) => {
                 write!(f, "EXPR ")?;
 
-                // Check if it's `wN - C = 0` and print it as `wN = C`,
-                // or if its' `wN + C = 0` and print it as `wN = -C`.
+                // Check if it's `w - C = 0` and print it as `w = C`,
+                // or if its' `w + C = 0` and print it as `w = -C`.
                 if expr.mul_terms.is_empty() && expr.linear_combinations.len() == 1 {
                     let (coefficient, witness) = expr.linear_combinations[0];
                     let constant = expr.q_c;
@@ -169,8 +169,8 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                     }
                 }
 
-                // Check if it's `-wN * wM = 0` or `wN * -wM = 0` in which case we can
-                // print it as `wN = wM`.
+                // Check if it's `-w1 * w2 = 0` or `w1 * -w2 = 0` in which case we can
+                // print it as `w1 = w2`.
                 if expr.mul_terms.is_empty()
                     && expr.linear_combinations.len() == 2
                     && expr.q_c.is_zero()
@@ -186,6 +186,31 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                     }
                 }
 
+                // Check if it's `c1*w1*w2 - w3 = 0` or similar, in which case we can print it
+                // as `w1 = c1*w2*w3`.
+                if expr.mul_terms.len() == 1
+                    && expr.linear_combinations.len() == 1
+                    && expr.q_c.is_zero()
+                {
+                    let (coefficient1, witness1, witness2) = expr.mul_terms[0];
+                    let (coefficient2, witness3) = expr.linear_combinations[0];
+                    if witness1 != witness3
+                        && witness2 != witness3
+                        && (coefficient2.is_one() || (-coefficient2).is_one())
+                    {
+                        let coefficient1 =
+                            if coefficient2.is_one() { -coefficient1 } else { coefficient1 };
+                        if coefficient1.is_one() {
+                            write!(f, "{witness3} = {witness1}*{witness2}")?;
+                        } else if (-coefficient1).is_one() {
+                            write!(f, "{witness3} = -{witness1}*{witness2}")?;
+                        } else {
+                            write!(f, "{witness3} = {coefficient1}*{witness1}*{witness2}")?;
+                        }
+                        return Ok(());
+                    }
+                }
+
                 let mut printed_term = false;
 
                 for (coefficient, witness1, witness2) in &expr.mul_terms {
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 9e31399f246..bcd1ad72de1 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -1,3 +1,5 @@
+use insta::assert_snapshot;
+
 use crate::{
     circuit::{Circuit, Program},
     parser::ParserError,
@@ -118,10 +120,10 @@ fn assert_zero_with_mul_terms() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    EXPR w0*w1 - w3 = 0
-    EXPR w3*w3 - w4 = 0
-    EXPR w4*w4 - w5 = 0
-    EXPR w5*w5 - w6 = 0
+    EXPR w3 = w0*w1
+    EXPR w4 = w3*w3
+    EXPR w5 = w4*w4
+    EXPR w6 = w5*w5
     EXPR w2 = w6
     ";
     assert_circuit_roundtrip(src);
@@ -656,7 +658,7 @@ fn array_dynamic() {
     MEM (id: 3, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w49) ])
     MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w50) ])
     EXPR -w31*w36 = 0
-    EXPR w21*w31 - w51 = 0
+    EXPR w51 = w21*w31
     MEM (id: 0, read at: EXPR [ (1, w51) ], value: EXPR [ (1, w52) ])
     EXPR -w31*w52 + w52 - w53 = 0
     MEM (id: 0, write EXPR [ (1, w53) ] at: EXPR [ (1, w51) ])
@@ -751,3 +753,22 @@ fn fold_basic_mismatched_ids() {
     assert_eq!(expected, 1);
     assert_eq!(found, 2);
 }
+
+#[test]
+fn assert_zero_equation() {
+    let src = "
+    current witness: w9
+    private parameters: [w0, w1, w2, w2]
+    public parameters: []
+    return values: []
+    EXPR - w0 + w1 - 10 + 20 + w0*w2 = w2 - w3 + w0*w1 - w1*w2 - 30
+    ";
+    let circuit = Circuit::from_str(src).unwrap();
+    assert_snapshot!(circuit.to_string(), @r"
+    current witness: w9
+    private parameters: [w0, w1, w2]
+    public parameters: []
+    return values: []
+    EXPR w0*w2 - w0*w1 + w1*w2 - w0 + w1 - w2 + w3 = -40
+    ");
+}
diff --git a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
index a74f07ca8a1..35636d5c830 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
@@ -348,7 +348,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR w0*w1 + w5 = 0
+        EXPR w5 = -w0*w1
         EXPR 2*w0*w0 - w3 + 2*w5 = 0
         BLACKBOX::RANGE [w3]:32 bits []
         ");
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index 0b75317345f..1e2df87929b 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -161,7 +161,7 @@ fn generates_predicated_index_for_dynamic_read() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR w3*w4 - w5 = 0
+    EXPR w5 = w3*w4
     MEM (id: 0, read at: EXPR [ (1, w5) ], value: EXPR [ (1, w6) ])
     EXPR w6 = 10
     ");
@@ -199,7 +199,7 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR w3*w4 - w8 = 0
+    EXPR w8 = w3*w4
     MEM (id: 0, read at: EXPR [ (1, w8) ], value: EXPR [ (1, w9) ])
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
     EXPR -w4*w9 + 10*w4 + w9 - w10 = 0
diff --git a/compiler/noirc_evaluator/src/acir/tests/mod.rs b/compiler/noirc_evaluator/src/acir/tests/mod.rs
index a72290ce958..7d639e4f2ab 100644
--- a/compiler/noirc_evaluator/src/acir/tests/mod.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/mod.rs
@@ -95,7 +95,7 @@ fn unchecked_mul_should_not_have_range_check() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR -w0*w1 + w2 = 0
+    EXPR w2 = w0*w1
     ");
 }
 

From 56c48f0e1e459644b419edcdbaf84e580e445a6a Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Thu, 25 Sep 2025 10:28:35 -0300
Subject: [PATCH 17/25] Don't simplify too much

---
 acvm-repo/acir/src/circuit/mod.rs             |  2 +-
 acvm-repo/acir/src/circuit/opcodes.rs         | 50 +++----------------
 acvm-repo/acir/src/parser/tests.rs            | 44 ++++++++--------
 .../compiler/optimizers/merge_expressions.rs  |  2 +-
 .../noirc_evaluator/src/acir/tests/arrays.rs  |  4 +-
 .../src/acir/tests/brillig_call.rs            | 26 +++++-----
 .../noirc_evaluator/src/acir/tests/call.rs    |  2 +-
 .../noirc_evaluator/src/acir/tests/mod.rs     |  2 +-
 8 files changed, 49 insertions(+), 83 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/mod.rs b/acvm-repo/acir/src/circuit/mod.rs
index 85056107edc..1dd1e2f8bb0 100644
--- a/acvm-repo/acir/src/circuit/mod.rs
+++ b/acvm-repo/acir/src/circuit/mod.rs
@@ -544,7 +544,7 @@ mod tests {
         private parameters: []
         public parameters: [w2]
         return values: [w2]
-        EXPR 2*w1 = -8
+        EXPR 2*w1 + 8 = 0
         BLACKBOX::RANGE [w1]:8 bits []
         BLACKBOX::AND [w1, w2]:4 bits [w3]
         BLACKBOX::KECCAKF1600 [w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25] [w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43, w44, w45, w46, w47, w48, w49, w50]
diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index 90b6f3a1e51..e4b518323ed 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -153,17 +153,8 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                 // or if its' `w + C = 0` and print it as `w = -C`.
                 if expr.mul_terms.is_empty() && expr.linear_combinations.len() == 1 {
                     let (coefficient, witness) = expr.linear_combinations[0];
-                    let constant = expr.q_c;
-
-                    if coefficient.is_one() {
-                        // This is `wN + C = 0`, so show it as `wN = -C`.
-                        let constant = -constant;
-                        write!(f, "{witness} = {constant}")?;
-                        return Ok(());
-                    }
-
-                    if (-coefficient).is_one() {
-                        // This is `-wN + C = 0`, so show it as `wN = C`.
+                    if coefficient.is_one() || (-coefficient).is_one() {
+                        let constant = if coefficient.is_one() { -expr.q_c } else { expr.q_c };
                         write!(f, "{witness} = {constant}")?;
                         return Ok(());
                     }
@@ -186,31 +177,6 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                     }
                 }
 
-                // Check if it's `c1*w1*w2 - w3 = 0` or similar, in which case we can print it
-                // as `w1 = c1*w2*w3`.
-                if expr.mul_terms.len() == 1
-                    && expr.linear_combinations.len() == 1
-                    && expr.q_c.is_zero()
-                {
-                    let (coefficient1, witness1, witness2) = expr.mul_terms[0];
-                    let (coefficient2, witness3) = expr.linear_combinations[0];
-                    if witness1 != witness3
-                        && witness2 != witness3
-                        && (coefficient2.is_one() || (-coefficient2).is_one())
-                    {
-                        let coefficient1 =
-                            if coefficient2.is_one() { -coefficient1 } else { coefficient1 };
-                        if coefficient1.is_one() {
-                            write!(f, "{witness3} = {witness1}*{witness2}")?;
-                        } else if (-coefficient1).is_one() {
-                            write!(f, "{witness3} = -{witness1}*{witness2}")?;
-                        } else {
-                            write!(f, "{witness3} = {coefficient1}*{witness1}*{witness2}")?;
-                        }
-                        return Ok(());
-                    }
-                }
-
                 let mut printed_term = false;
 
                 for (coefficient, witness1, witness2) in &expr.mul_terms {
@@ -271,12 +237,12 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                     printed_term = true;
                 }
 
-                if printed_term {
-                    // Change `... + c = 0` to `... = -c`
-                    let q_c = -expr.q_c;
-                    write!(f, " = {q_c}")?;
-                } else if expr.q_c.is_zero() {
-                    write!(f, "0 = 0")?;
+                if expr.q_c.is_zero() {
+                    if printed_term {
+                        write!(f, " = 0")?;
+                    } else {
+                        write!(f, "0 = 0")?;
+                    }
                 } else {
                     let coefficient = expr.q_c;
                     let coefficient_as_string = coefficient.to_string();
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index bcd1ad72de1..5afdcd43114 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -120,10 +120,10 @@ fn assert_zero_with_mul_terms() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    EXPR w3 = w0*w1
-    EXPR w4 = w3*w3
-    EXPR w5 = w4*w4
-    EXPR w6 = w5*w5
+    EXPR -w0*w1 + w3 = 0
+    EXPR -w3*w3 + w4 = 0
+    EXPR -w4*w4 + w5 = 0
+    EXPR -w5*w5 + w6 = 0
     EXPR w2 = w6
     ";
     assert_circuit_roundtrip(src);
@@ -527,7 +527,7 @@ fn brillig_call() {
     public parameters: []
     return values: []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
-    EXPR w0*w3 - w1*w3 = 1
+    EXPR w0*w3 - w1*w3 - 1 = 0
     EXPR w0 = w2
     ";
     assert_circuit_roundtrip(src);
@@ -542,7 +542,7 @@ fn brillig_call_with_predicate() {
     return values: []
     BRILLIG CALL func 0: PREDICATE: EXPR [ 1 ]
     inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
-    EXPR w0*w3 - w1*w3 = 1
+    EXPR w0*w3 - w1*w3 - 1 = 0
     EXPR w0 = w2
     ";
     assert_circuit_roundtrip(src);
@@ -612,15 +612,15 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w19]:32 bits []
     EXPR w5 - w19 - w20 = 0
     BLACKBOX::RANGE [w20]:32 bits []
-    EXPR w20 - w21 = 5
-    EXPR w21 - w22 = 3
+    EXPR w20 - w21 - 5 = 0
+    EXPR w21 - w22 - 3 = 0
     MEM (id: 0, read at: EXPR [ (1, w21) ], value: EXPR [ (1, w23) ])
     EXPR w23 = 111
     MEM (id: 0, read at: EXPR [ (1, w22) ], value: EXPR [ (1, w24) ])
     EXPR w24 = 101
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w22) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w25, w26]
     BLACKBOX::RANGE [w26]:32 bits []
-    EXPR w22 - 4294967296*w25 - w26 = -4294967291
+    EXPR w22 - 4294967296*w25 - w26 + 4294967291 = 0
     EXPR w25 = 0
     EXPR w27 = 0
     MEM (id: 0, write EXPR [ (1, w27) ] at: EXPR [ (1, w22) ])
@@ -632,15 +632,15 @@ fn array_dynamic() {
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967286 ], EXPR [ 4294967296 ]], outputs: [w31, w32]
     BLACKBOX::RANGE [w31]:1 bits []
     BLACKBOX::RANGE [w32]:32 bits []
-    EXPR w21 - 4294967296*w31 - w32 = -4294967286
+    EXPR w21 - 4294967296*w31 - w32 + 4294967286 = 0
     EXPR -w21*w31 + w21 - w33 = 0
     MEM (id: 0, read at: EXPR [ (1, w33) ], value: EXPR [ (1, w34) ])
-    EXPR -w31*w34 + 2*w31 + w34 - w35 = 2
+    EXPR -w31*w34 + 2*w31 + w34 - w35 - 2 = 0
     BLACKBOX::RANGE [w35]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w36, w37]
     BLACKBOX::RANGE [w36]:1 bits []
     BLACKBOX::RANGE [w37]:32 bits []
-    EXPR w21 - 4294967296*w36 - w37 = -4294967291
+    EXPR w21 - 4294967296*w36 - w37 + 4294967291 = 0
     EXPR w31*w36 - w36 = 0
     EXPR -w21*w31 + w21 - w38 = 0
     MEM (id: 0, read at: EXPR [ (1, w38) ], value: EXPR [ (1, w39) ])
@@ -658,14 +658,14 @@ fn array_dynamic() {
     MEM (id: 3, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w49) ])
     MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w50) ])
     EXPR -w31*w36 = 0
-    EXPR w51 = w21*w31
+    EXPR -w21*w31 + w51 = 0
     MEM (id: 0, read at: EXPR [ (1, w51) ], value: EXPR [ (1, w52) ])
     EXPR -w31*w52 + w52 - w53 = 0
     MEM (id: 0, write EXPR [ (1, w53) ] at: EXPR [ (1, w51) ])
     MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w54) ])
-    EXPR -w31 - w55 = -1
+    EXPR -w31 - w55 + 1 = 0
     EXPR -w31*w49 + w31*w50 + w49 - w56 = 0
-    EXPR w31*w54 + w55*w56 = 109
+    EXPR w31*w54 + w55*w56 - 109 = 0
     EXPR w57 = 246
     EXPR w58 = 159
     EXPR w59 = 32
@@ -678,23 +678,23 @@ fn array_dynamic() {
     MEM (id: 4, read at: EXPR [ (1, w10) ], value: EXPR [ (1, w65) ])
     MEM (id: 4, read at: EXPR [ (1, w11) ], value: EXPR [ (1, w66) ])
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w62) (1, w63) (1, w64) (1, w65) (1, w66) ]], outputs: [w67]
-    EXPR w62*w67 + w63*w67 + w64*w67 + w65*w67 + w66*w67 = 1
+    EXPR w62*w67 + w63*w67 + w64*w67 + w65*w67 + w66*w67 - 1 = 0
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w18) ], EXPR [ 4294967296 ]], outputs: [w68, w69]
     BLACKBOX::RANGE [w68]:222 bits []
     BLACKBOX::RANGE [w69]:32 bits []
     EXPR w18 - 4294967296*w68 - w69 = 0
-    EXPR -w68 - w70 = -5096253676302562286669017222071363378443840053029366383258766538131
+    EXPR -w68 - w70 + 5096253676302562286669017222071363378443840053029366383258766538131 = 0
     BLACKBOX::RANGE [w70]:222 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (-1, w68) 5096253676302562286669017222071363378443840053029366383258766538131 ]], outputs: [w71]
-    EXPR -w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + w72 = 1
+    EXPR -w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + w72 - 1 = 0
     EXPR -w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72 = 0
     EXPR w69*w72 + 268435455*w72 - w73 = 0
     BLACKBOX::RANGE [w73]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (-1, w69) 4294967299 ], EXPR [ 4294967296 ]], outputs: [w74, w75]
     BLACKBOX::RANGE [w74]:1 bits []
     BLACKBOX::RANGE [w75]:32 bits []
-    EXPR -w69 - 4294967296*w74 - w75 = -4294967299
-    EXPR -w17*w74 + w17 - 3*w74 - w76 = -3
+    EXPR -w69 - 4294967296*w74 - w75 + 4294967299 = 0
+    EXPR -w17*w74 + w17 - 3*w74 - w76 + 3 = 0
     BLACKBOX::RANGE [w76]:32 bits []
     EXPR -w74*w76 + w76 - w77 = 0
     MEM (id: 1, read at: EXPR [ (1, w77) ], value: EXPR [ (1, w78) ])
@@ -720,7 +720,7 @@ fn fold_basic() {
     public parameters: []
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
-    EXPR w0*w3 - w1*w3 = 1
+    EXPR w0*w3 - w1*w3 - 1 = 0
     EXPR w0 = w2
     ";
     assert_program_roundtrip(src);
@@ -769,6 +769,6 @@ fn assert_zero_equation() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    EXPR w0*w2 - w0*w1 + w1*w2 - w0 + w1 - w2 + w3 = -40
+    EXPR w0*w2 - w0*w1 + w1*w2 - w0 + w1 - w2 + w3 + 40 = 0
     ");
 }
diff --git a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
index 35636d5c830..a74f07ca8a1 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
@@ -348,7 +348,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR w5 = -w0*w1
+        EXPR w0*w1 + w5 = 0
         EXPR 2*w0*w0 - w3 + 2*w5 = 0
         BLACKBOX::RANGE [w3]:32 bits []
         ");
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index 1e2df87929b..0b75317345f 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -161,7 +161,7 @@ fn generates_predicated_index_for_dynamic_read() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR w5 = w3*w4
+    EXPR w3*w4 - w5 = 0
     MEM (id: 0, read at: EXPR [ (1, w5) ], value: EXPR [ (1, w6) ])
     EXPR w6 = 10
     ");
@@ -199,7 +199,7 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR w8 = w3*w4
+    EXPR w3*w4 - w8 = 0
     MEM (id: 0, read at: EXPR [ (1, w8) ], value: EXPR [ (1, w9) ])
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
     EXPR -w4*w9 + 10*w4 + w9 - w10 = 0
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index 049cfef5c26..cac103cfb96 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -153,19 +153,19 @@ fn multiple_brillig_stdlib_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
-    EXPR w1*w3 = 1
+    EXPR w1*w3 - 1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 - w5 - w6 = 1
+    EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
     EXPR w2 = w4
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) ]], outputs: [w7]
-    EXPR w2*w7 = 1
+    EXPR w2*w7 - 1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w8, w9]
     BLACKBOX::RANGE [w9]:32 bits []
-    EXPR w2 - w9 - w10 = 1
+    EXPR w2 - w9 - w10 - 1 = 0
     BLACKBOX::RANGE [w10]:32 bits []
     EXPR -w2*w8 + w1 - w9 = 0
     EXPR w8 = 1
@@ -241,11 +241,11 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
-    EXPR w1*w3 = 1
+    EXPR w1*w3 - 1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 - w5 - w6 = 1
+    EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
     EXPR w2 = w4
@@ -254,10 +254,10 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w8]
     BLACKBOX::RANGE [w8]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) ]], outputs: [w9]
-    EXPR w2*w9 = 1
+    EXPR w2*w9 - 1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w10, w11]
     BLACKBOX::RANGE [w11]:32 bits []
-    EXPR w2 - w11 - w12 = 1
+    EXPR w2 - w11 - w12 - 1 = 0
     BLACKBOX::RANGE [w12]:32 bits []
     EXPR -w2*w10 + w1 - w11 = 0
     EXPR w10 = 1
@@ -375,11 +375,11 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
-    EXPR w1*w3 = 1
+    EXPR w1*w3 - 1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 - w5 - w6 = 1
+    EXPR w1 - w5 - w6 - 1 = 0
     BLACKBOX::RANGE [w6]:32 bits []
     EXPR -w1*w4 + w0 - w5 = 0
     EXPR w2 = w4
@@ -390,10 +390,10 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w9]
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) ]], outputs: [w10]
-    EXPR w2*w10 = 1
+    EXPR w2*w10 - 1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w11, w12]
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR w2 - w12 - w13 = 1
+    EXPR w2 - w12 - w13 - 1 = 0
     BLACKBOX::RANGE [w13]:32 bits []
     EXPR -w2*w11 + w1 - w12 = 0
     EXPR w11 = 1
@@ -407,7 +407,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     EXPR w0 - w1 - w3 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w3) ]], outputs: [w4]
-    EXPR w3*w4 + w5 = 1
+    EXPR w3*w4 + w5 - 1 = 0
     EXPR w3*w5 = 0
     EXPR w5 = 0
     EXPR w0 = w2
diff --git a/compiler/noirc_evaluator/src/acir/tests/call.rs b/compiler/noirc_evaluator/src/acir/tests/call.rs
index a9b59ff6478..b7b7fff5a2d 100644
--- a/compiler/noirc_evaluator/src/acir/tests/call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/call.rs
@@ -161,7 +161,7 @@ fn basic_nested_call(inline_type: InlineType) {
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 - w3 = -2
+    EXPR w0 - w3 + 2 = 0
     CALL func 2: PREDICATE: EXPR [ 1 ]
     inputs: [w3, w1], outputs: [w4]
     EXPR w2 = w4
diff --git a/compiler/noirc_evaluator/src/acir/tests/mod.rs b/compiler/noirc_evaluator/src/acir/tests/mod.rs
index 7d639e4f2ab..a72290ce958 100644
--- a/compiler/noirc_evaluator/src/acir/tests/mod.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/mod.rs
@@ -95,7 +95,7 @@ fn unchecked_mul_should_not_have_range_check() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR w2 = w0*w1
+    EXPR -w0*w1 + w2 = 0
     ");
 }
 

From 257818be292a89cf2ea3efe8575c928fed4e1aaf Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Thu, 25 Sep 2025 11:17:33 -0300
Subject: [PATCH 18/25] Show AssertZero based on actual code

---
 acvm-repo/acir/src/circuit/opcodes.rs         |  91 +++++++++------
 acvm-repo/acir/src/parser/tests.rs            | 108 +++++++++---------
 .../compiler/optimizers/merge_expressions.rs  |   4 +-
 .../noirc_evaluator/src/acir/tests/arrays.rs  |  18 +--
 .../src/acir/tests/brillig_call.rs            |  36 +++---
 .../noirc_evaluator/src/acir/tests/call.rs    |   6 +-
 .../noirc_evaluator/src/acir/tests/mod.rs     |   2 +-
 7 files changed, 142 insertions(+), 123 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index e4b518323ed..5e721044369 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -149,37 +149,39 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
             Opcode::AssertZero(expr) => {
                 write!(f, "EXPR ")?;
 
-                // Check if it's `w - C = 0` and print it as `w = C`,
-                // or if its' `w + C = 0` and print it as `w = -C`.
-                if expr.mul_terms.is_empty() && expr.linear_combinations.len() == 1 {
-                    let (coefficient, witness) = expr.linear_combinations[0];
-                    if coefficient.is_one() || (-coefficient).is_one() {
-                        let constant = if coefficient.is_one() { -expr.q_c } else { expr.q_c };
-                        write!(f, "{witness} = {constant}")?;
-                        return Ok(());
-                    }
-                }
-
-                // Check if it's `-w1 * w2 = 0` or `w1 * -w2 = 0` in which case we can
-                // print it as `w1 = w2`.
-                if expr.mul_terms.is_empty()
-                    && expr.linear_combinations.len() == 2
-                    && expr.q_c.is_zero()
-                {
-                    let (coefficient1, witness1) = expr.linear_combinations[0];
-                    let (coefficient2, witness2) = expr.linear_combinations[1];
-
-                    if (coefficient1.is_one() && (-coefficient2).is_one())
-                        || ((-coefficient1).is_one() && coefficient2.is_one())
-                    {
-                        write!(f, "{witness1} = {witness2}")?;
-                        return Ok(());
-                    }
+                // This is set to an index if we show this expression "as an assignment", meaning
+                // that the linear combination at this index must not be printed again.
+                let mut show_as_assignment: Option<usize> = None;
+
+                // If true, negate all coefficients when printing.
+                // This is set to true if we show this expression "as an assignment", and the witness
+                // had a coefficient of 1 and we "moved" everything to the right of the equal sign.
+                let mut negate_coefficients = false;
+
+                // Find a linear combination with a coefficient of 1 or -1 and, if there are many,
+                // keep the one with the largest witness.
+                let linear_witness_one = expr
+                    .linear_combinations
+                    .iter()
+                    .enumerate()
+                    .filter(|(_, (coefficient, _))| {
+                        coefficient.is_one() || (-*coefficient).is_one()
+                    })
+                    .max_by_key(|(_, (_, witness))| witness);
+
+                // If we find one, show the expression as equaling this witness to everything else
+                // (this is likely to happen as in ACIR gen we tend to equate a witness to previous expressions)
+                if let Some((index, (coefficient, witness))) = linear_witness_one {
+                    show_as_assignment = Some(index);
+                    negate_coefficients = coefficient.is_one();
+                    write!(f, "{witness} = ")?;
                 }
 
                 let mut printed_term = false;
 
                 for (coefficient, witness1, witness2) in &expr.mul_terms {
+                    let coefficient =
+                        if negate_coefficients { -*coefficient } else { *coefficient };
                     let coefficient_as_string = coefficient.to_string();
                     let coefficient_is_negative = coefficient_as_string.starts_with('-');
 
@@ -192,9 +194,9 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                     }
 
                     let coefficient = if printed_term && coefficient_is_negative {
-                        -*coefficient
+                        -coefficient
                     } else {
-                        *coefficient
+                        coefficient
                     };
 
                     if coefficient.is_one() {
@@ -208,7 +210,16 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                     printed_term = true;
                 }
 
-                for (coefficient, witness) in &expr.linear_combinations {
+                for (index, (coefficient, witness)) in expr.linear_combinations.iter().enumerate() {
+                    if show_as_assignment
+                        .is_some_and(|show_as_assignment_index| show_as_assignment_index == index)
+                    {
+                        // We already printed this term as part of the assignment
+                        continue;
+                    }
+
+                    let coefficient =
+                        if negate_coefficients { -*coefficient } else { *coefficient };
                     let coefficient_as_string = coefficient.to_string();
                     let coefficient_is_negative = coefficient_as_string.starts_with('-');
 
@@ -221,9 +232,9 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                     }
 
                     let coefficient = if printed_term && coefficient_is_negative {
-                        -*coefficient
+                        -coefficient
                     } else {
-                        *coefficient
+                        coefficient
                     };
 
                     if coefficient.is_one() {
@@ -238,13 +249,18 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                 }
 
                 if expr.q_c.is_zero() {
-                    if printed_term {
-                        write!(f, " = 0")?;
-                    } else {
-                        write!(f, "0 = 0")?;
+                    if show_as_assignment.is_none() {
+                        if printed_term {
+                            write!(f, " = 0")?;
+                        } else {
+                            write!(f, "0 = 0")?;
+                        }
+                    } else if !printed_term {
+                        write!(f, "0")?;
                     }
                 } else {
                     let coefficient = expr.q_c;
+                    let coefficient = if negate_coefficients { -coefficient } else { coefficient };
                     let coefficient_as_string = coefficient.to_string();
                     let coefficient_is_negative = coefficient_as_string.starts_with('-');
 
@@ -262,7 +278,10 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                         coefficient
                     };
                     write!(f, "{coefficient}")?;
-                    write!(f, " = 0")?;
+
+                    if show_as_assignment.is_none() {
+                        write!(f, " = 0")?;
+                    }
                 }
 
                 Ok(())
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 5afdcd43114..41e9488ccc7 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -104,11 +104,11 @@ fn assert_zero_opcodes() {
     private parameters: [w0, w1, w2, w3, w4]
     public parameters: [w5, w6, w7, w8, w9]
     return values: []
-    EXPR w0 = w5
-    EXPR w1 = w6
-    EXPR w2 = w7
-    EXPR w3 = w8
-    EXPR w4 = w9
+    EXPR w5 = w0
+    EXPR w6 = w1
+    EXPR w7 = w2
+    EXPR w8 = w3
+    EXPR w9 = w4
     ";
     assert_circuit_roundtrip(src);
 }
@@ -120,11 +120,11 @@ fn assert_zero_with_mul_terms() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    EXPR -w0*w1 + w3 = 0
-    EXPR -w3*w3 + w4 = 0
-    EXPR -w4*w4 + w5 = 0
-    EXPR -w5*w5 + w6 = 0
-    EXPR w2 = w6
+    EXPR w3 = w0*w1
+    EXPR w4 = w3*w3
+    EXPR w5 = w4*w4
+    EXPR w6 = w5*w5
+    EXPR w6 = w2
     ";
     assert_circuit_roundtrip(src);
 }
@@ -225,22 +225,22 @@ fn aes128_encrypt() {
     BLACKBOX::RANGE [w58]:8 bits []
     BLACKBOX::RANGE [w59]:8 bits []
     BLACKBOX::AES128_ENCRYPT [w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43] [w60, w61, w62, w63, w64, w65, w66, w67, w68, w69, w70, w71, w72, w73, w74, w75]
-    EXPR w44 = w60
-    EXPR w45 = w61
-    EXPR w46 = w62
-    EXPR w47 = w63
-    EXPR w48 = w64
-    EXPR w49 = w65
-    EXPR w50 = w66
-    EXPR w51 = w67
-    EXPR w52 = w68
-    EXPR w53 = w69
-    EXPR w54 = w70
-    EXPR w55 = w71
-    EXPR w56 = w72
-    EXPR w57 = w73
-    EXPR w58 = w74
-    EXPR w59 = w75
+    EXPR w60 = w44
+    EXPR w61 = w45
+    EXPR w62 = w46
+    EXPR w63 = w47
+    EXPR w64 = w48
+    EXPR w65 = w49
+    EXPR w66 = w50
+    EXPR w67 = w51
+    EXPR w68 = w52
+    EXPR w69 = w53
+    EXPR w70 = w54
+    EXPR w71 = w55
+    EXPR w72 = w56
+    EXPR w73 = w57
+    EXPR w74 = w58
+    EXPR w75 = w59
     ";
     assert_circuit_roundtrip(src);
 }
@@ -528,7 +528,7 @@ fn brillig_call() {
     return values: []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
-    EXPR w0 = w2
+    EXPR w2 = w0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -543,7 +543,7 @@ fn brillig_call_with_predicate() {
     BRILLIG CALL func 0: PREDICATE: EXPR [ 1 ]
     inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
-    EXPR w0 = w2
+    EXPR w2 = w0
     ";
     assert_circuit_roundtrip(src);
 }
@@ -608,19 +608,19 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w15]:32 bits []
     BLACKBOX::RANGE [w16]:32 bits []
     BLACKBOX::RANGE [w17]:32 bits []
-    EXPR 5*w6 - w19 = 0
+    EXPR w19 = 5*w6
     BLACKBOX::RANGE [w19]:32 bits []
-    EXPR w5 - w19 - w20 = 0
+    EXPR w20 = w5 - w19
     BLACKBOX::RANGE [w20]:32 bits []
-    EXPR w20 - w21 - 5 = 0
-    EXPR w21 - w22 - 3 = 0
+    EXPR w21 = w20 - 5
+    EXPR w22 = w21 - 3
     MEM (id: 0, read at: EXPR [ (1, w21) ], value: EXPR [ (1, w23) ])
     EXPR w23 = 111
     MEM (id: 0, read at: EXPR [ (1, w22) ], value: EXPR [ (1, w24) ])
     EXPR w24 = 101
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w22) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w25, w26]
     BLACKBOX::RANGE [w26]:32 bits []
-    EXPR w22 - 4294967296*w25 - w26 + 4294967291 = 0
+    EXPR w26 = w22 - 4294967296*w25 + 4294967291
     EXPR w25 = 0
     EXPR w27 = 0
     MEM (id: 0, write EXPR [ (1, w27) ] at: EXPR [ (1, w22) ])
@@ -632,17 +632,17 @@ fn array_dynamic() {
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967286 ], EXPR [ 4294967296 ]], outputs: [w31, w32]
     BLACKBOX::RANGE [w31]:1 bits []
     BLACKBOX::RANGE [w32]:32 bits []
-    EXPR w21 - 4294967296*w31 - w32 + 4294967286 = 0
-    EXPR -w21*w31 + w21 - w33 = 0
+    EXPR w32 = w21 - 4294967296*w31 + 4294967286
+    EXPR w33 = -w21*w31 + w21
     MEM (id: 0, read at: EXPR [ (1, w33) ], value: EXPR [ (1, w34) ])
-    EXPR -w31*w34 + 2*w31 + w34 - w35 - 2 = 0
+    EXPR w35 = -w31*w34 + 2*w31 + w34 - 2
     BLACKBOX::RANGE [w35]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w21) 4294967291 ], EXPR [ 4294967296 ]], outputs: [w36, w37]
     BLACKBOX::RANGE [w36]:1 bits []
     BLACKBOX::RANGE [w37]:32 bits []
-    EXPR w21 - 4294967296*w36 - w37 + 4294967291 = 0
-    EXPR w31*w36 - w36 = 0
-    EXPR -w21*w31 + w21 - w38 = 0
+    EXPR w37 = w21 - 4294967296*w36 + 4294967291
+    EXPR w36 = w31*w36
+    EXPR w38 = -w21*w31 + w21
     MEM (id: 0, read at: EXPR [ (1, w38) ], value: EXPR [ (1, w39) ])
     MEM (id: 0, read at: EXPR [ (1, w27) ], value: EXPR [ (1, w40) ])
     MEM (id: 0, read at: EXPR [ (1, w29) ], value: EXPR [ (1, w41) ])
@@ -653,18 +653,18 @@ fn array_dynamic() {
     EXPR w46 = 0
     MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w47) ])
     INIT (id: 3, len: 5, witnesses: [w40, w41, w43, w45, w47])
-    EXPR -w31*w35 + w31*w39 + w35 - w48 = 0
+    EXPR w48 = -w31*w35 + w31*w39 + w35
     MEM (id: 3, write EXPR [ (1, w48) ] at: EXPR [ (1, w38) ])
     MEM (id: 3, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w49) ])
     MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w50) ])
     EXPR -w31*w36 = 0
-    EXPR -w21*w31 + w51 = 0
+    EXPR w51 = w21*w31
     MEM (id: 0, read at: EXPR [ (1, w51) ], value: EXPR [ (1, w52) ])
-    EXPR -w31*w52 + w52 - w53 = 0
+    EXPR w53 = -w31*w52 + w52
     MEM (id: 0, write EXPR [ (1, w53) ] at: EXPR [ (1, w51) ])
     MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w54) ])
-    EXPR -w31 - w55 + 1 = 0
-    EXPR -w31*w49 + w31*w50 + w49 - w56 = 0
+    EXPR w55 = -w31 + 1
+    EXPR w56 = -w31*w49 + w31*w50 + w49
     EXPR w31*w54 + w55*w56 - 109 = 0
     EXPR w57 = 246
     EXPR w58 = 159
@@ -682,23 +682,23 @@ fn array_dynamic() {
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w18) ], EXPR [ 4294967296 ]], outputs: [w68, w69]
     BLACKBOX::RANGE [w68]:222 bits []
     BLACKBOX::RANGE [w69]:32 bits []
-    EXPR w18 - 4294967296*w68 - w69 = 0
-    EXPR -w68 - w70 + 5096253676302562286669017222071363378443840053029366383258766538131 = 0
+    EXPR w69 = w18 - 4294967296*w68
+    EXPR w70 = -w68 + 5096253676302562286669017222071363378443840053029366383258766538131
     BLACKBOX::RANGE [w70]:222 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (-1, w68) 5096253676302562286669017222071363378443840053029366383258766538131 ]], outputs: [w71]
-    EXPR -w68*w71 + 5096253676302562286669017222071363378443840053029366383258766538131*w71 + w72 - 1 = 0
+    EXPR w72 = w68*w71 - 5096253676302562286669017222071363378443840053029366383258766538131*w71 + 1
     EXPR -w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72 = 0
-    EXPR w69*w72 + 268435455*w72 - w73 = 0
+    EXPR w73 = w69*w72 + 268435455*w72
     BLACKBOX::RANGE [w73]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (-1, w69) 4294967299 ], EXPR [ 4294967296 ]], outputs: [w74, w75]
     BLACKBOX::RANGE [w74]:1 bits []
     BLACKBOX::RANGE [w75]:32 bits []
-    EXPR -w69 - 4294967296*w74 - w75 + 4294967299 = 0
-    EXPR -w17*w74 + w17 - 3*w74 - w76 + 3 = 0
+    EXPR w75 = -w69 - 4294967296*w74 + 4294967299
+    EXPR w76 = -w17*w74 + w17 - 3*w74 + 3
     BLACKBOX::RANGE [w76]:32 bits []
-    EXPR -w74*w76 + w76 - w77 = 0
+    EXPR w77 = -w74*w76 + w76
     MEM (id: 1, read at: EXPR [ (1, w77) ], value: EXPR [ (1, w78) ])
-    EXPR w15*w74 - w74*w78 - w15 + w78 = 0
+    EXPR w78 = -w15*w74 + w74*w78 + w15
     ";
     assert_circuit_roundtrip(src);
 }
@@ -721,7 +721,7 @@ fn fold_basic() {
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
     EXPR w0*w3 - w1*w3 - 1 = 0
-    EXPR w0 = w2
+    EXPR w2 = w0
     ";
     assert_program_roundtrip(src);
 }
@@ -769,6 +769,6 @@ fn assert_zero_equation() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    EXPR w0*w2 - w0*w1 + w1*w2 - w0 + w1 - w2 + w3 + 40 = 0
+    EXPR w3 = -w0*w2 + w0*w1 - w1*w2 + w0 - w1 + w2 - 40
     ");
 }
diff --git a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
index a74f07ca8a1..7d13dfbe427 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/merge_expressions.rs
@@ -348,8 +348,8 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR w0*w1 + w5 = 0
-        EXPR 2*w0*w0 - w3 + 2*w5 = 0
+        EXPR w5 = -w0*w1
+        EXPR w3 = 2*w0*w0 + 2*w5
         BLACKBOX::RANGE [w3]:32 bits []
         ");
     }
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index 0b75317345f..231db2fb085 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -128,9 +128,9 @@ fn generates_memory_op_for_dynamic_write() {
     MEM (id: 1, read at: EXPR [ (1, w10) ], value: EXPR [ (1, w11) ])
     EXPR w12 = 2
     MEM (id: 1, read at: EXPR [ (1, w12) ], value: EXPR [ (1, w13) ])
-    EXPR w4 = w9
-    EXPR w5 = w11
-    EXPR w6 = w13
+    EXPR w9 = w4
+    EXPR w11 = w5
+    EXPR w13 = w6
     ");
 }
 
@@ -161,7 +161,7 @@ fn generates_predicated_index_for_dynamic_read() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR w3*w4 - w5 = 0
+    EXPR w5 = w3*w4
     MEM (id: 0, read at: EXPR [ (1, w5) ], value: EXPR [ (1, w6) ])
     EXPR w6 = 10
     ");
@@ -199,10 +199,10 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     INIT (id: 0, len: 3, witnesses: [w0, w1, w2])
     BLACKBOX::RANGE [w3]:32 bits []
     BLACKBOX::RANGE [w4]:1 bits []
-    EXPR w3*w4 - w8 = 0
+    EXPR w8 = w3*w4
     MEM (id: 0, read at: EXPR [ (1, w8) ], value: EXPR [ (1, w9) ])
     INIT (id: 1, len: 3, witnesses: [w0, w1, w2])
-    EXPR -w4*w9 + 10*w4 + w9 - w10 = 0
+    EXPR w10 = -w4*w9 + 10*w4 + w9
     MEM (id: 1, write EXPR [ (1, w10) ] at: EXPR [ (1, w8) ])
     EXPR w11 = 0
     MEM (id: 1, read at: EXPR [ (1, w11) ], value: EXPR [ (1, w12) ])
@@ -210,9 +210,9 @@ fn generates_predicated_index_and_dummy_value_for_dynamic_write() {
     MEM (id: 1, read at: EXPR [ (1, w13) ], value: EXPR [ (1, w14) ])
     EXPR w15 = 2
     MEM (id: 1, read at: EXPR [ (1, w15) ], value: EXPR [ (1, w16) ])
-    EXPR w5 = w12
-    EXPR w6 = w14
-    EXPR w7 = w16
+    EXPR w12 = w5
+    EXPR w14 = w6
+    EXPR w16 = w7
     ");
 }
 
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index cac103cfb96..8a7dd222bac 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -157,17 +157,17 @@ fn multiple_brillig_stdlib_calls() {
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 - w5 - w6 - 1 = 0
+    EXPR w6 = w1 - w5 - 1
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -w1*w4 + w0 - w5 = 0
-    EXPR w2 = w4
+    EXPR w5 = -w1*w4 + w0
+    EXPR w4 = w2
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) ]], outputs: [w7]
     EXPR w2*w7 - 1 = 0
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w8, w9]
     BLACKBOX::RANGE [w9]:32 bits []
-    EXPR w2 - w9 - w10 - 1 = 0
+    EXPR w10 = w2 - w9 - 1
     BLACKBOX::RANGE [w10]:32 bits []
-    EXPR -w2*w8 + w1 - w9 = 0
+    EXPR w9 = -w2*w8 + w1
     EXPR w8 = 1
 
     unconstrained func 0
@@ -245,10 +245,10 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 - w5 - w6 - 1 = 0
+    EXPR w6 = w1 - w5 - 1
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -w1*w4 + w0 - w5 = 0
-    EXPR w2 = w4
+    EXPR w5 = -w1*w4 + w0
+    EXPR w4 = w2
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w8]
@@ -257,9 +257,9 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     EXPR w2*w9 - 1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w10, w11]
     BLACKBOX::RANGE [w11]:32 bits []
-    EXPR w2 - w11 - w12 - 1 = 0
+    EXPR w12 = w2 - w11 - 1
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR -w2*w10 + w1 - w11 = 0
+    EXPR w11 = -w2*w10 + w1
     EXPR w10 = 1
 
     unconstrained func 0
@@ -379,10 +379,10 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
-    EXPR w1 - w5 - w6 - 1 = 0
+    EXPR w6 = w1 - w5 - 1
     BLACKBOX::RANGE [w6]:32 bits []
-    EXPR -w1*w4 + w0 - w5 = 0
-    EXPR w2 = w4
+    EXPR w5 = -w1*w4 + w0
+    EXPR w4 = w2
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w7]
     BLACKBOX::RANGE [w7]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w8]
@@ -393,9 +393,9 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     EXPR w2*w10 - 1 = 0
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w11, w12]
     BLACKBOX::RANGE [w12]:32 bits []
-    EXPR w2 - w12 - w13 - 1 = 0
+    EXPR w13 = w2 - w12 - 1
     BLACKBOX::RANGE [w13]:32 bits []
-    EXPR -w2*w11 + w1 - w12 = 0
+    EXPR w12 = -w2*w11 + w1
     EXPR w11 = 1
 
     func 1
@@ -405,12 +405,12 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR w0 - w1 - w3 = 0
+    EXPR w3 = w0 - w1
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w3) ]], outputs: [w4]
-    EXPR w3*w4 + w5 - 1 = 0
+    EXPR w5 = -w3*w4 + 1
     EXPR w3*w5 = 0
     EXPR w5 = 0
-    EXPR w0 = w2
+    EXPR w2 = w0
 
     unconstrained func 0
      0: @2 = const u32 1
diff --git a/compiler/noirc_evaluator/src/acir/tests/call.rs b/compiler/noirc_evaluator/src/acir/tests/call.rs
index b7b7fff5a2d..f8271d34788 100644
--- a/compiler/noirc_evaluator/src/acir/tests/call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/call.rs
@@ -64,15 +64,15 @@ fn basic_call_with_outputs_assert(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR w2 = w3
+    EXPR w3 = w2
 
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 = w1
-    EXPR w0 = w2
+    EXPR w1 = w0
+    EXPR w2 = w0
     ");
 }
 
diff --git a/compiler/noirc_evaluator/src/acir/tests/mod.rs b/compiler/noirc_evaluator/src/acir/tests/mod.rs
index a72290ce958..7d639e4f2ab 100644
--- a/compiler/noirc_evaluator/src/acir/tests/mod.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/mod.rs
@@ -95,7 +95,7 @@ fn unchecked_mul_should_not_have_range_check() {
     return values: [w2]
     BLACKBOX::RANGE [w0]:32 bits []
     BLACKBOX::RANGE [w1]:32 bits []
-    EXPR -w0*w1 + w2 = 0
+    EXPR w2 = w0*w1
     ");
 }
 

From 13f4812d5173f18230927926f136e03b6be4e0bf Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Thu, 25 Sep 2025 11:35:37 -0300
Subject: [PATCH 19/25] Fix snapshot

---
 compiler/noirc_evaluator/src/acir/tests/call.rs | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/compiler/noirc_evaluator/src/acir/tests/call.rs b/compiler/noirc_evaluator/src/acir/tests/call.rs
index f8271d34788..3ce187a7dc1 100644
--- a/compiler/noirc_evaluator/src/acir/tests/call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/call.rs
@@ -107,15 +107,15 @@ fn call_output_as_next_call_input(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w2, w1], outputs: [w3]
-    EXPR w2 = w3
+    EXPR w3 = w2
 
     func 1
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 = w1
-    EXPR w0 = w2
+    EXPR w1 = w0
+    EXPR w2 = w0
     ");
 }
 

From 4aec25957aec38eb7e7e4920098448d419521b84 Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Thu, 25 Sep 2025 11:35:44 -0300
Subject: [PATCH 20/25] Extract `display_term`

---
 acvm-repo/acir/src/circuit/opcodes.rs | 98 ++++++++++++---------------
 1 file changed, 44 insertions(+), 54 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index 5e721044369..7e81d4d02ed 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -180,33 +180,8 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                 let mut printed_term = false;
 
                 for (coefficient, witness1, witness2) in &expr.mul_terms {
-                    let coefficient =
-                        if negate_coefficients { -*coefficient } else { *coefficient };
-                    let coefficient_as_string = coefficient.to_string();
-                    let coefficient_is_negative = coefficient_as_string.starts_with('-');
-
-                    if printed_term {
-                        if coefficient_is_negative {
-                            write!(f, " - ")?;
-                        } else {
-                            write!(f, " + ")?;
-                        }
-                    }
-
-                    let coefficient = if printed_term && coefficient_is_negative {
-                        -coefficient
-                    } else {
-                        coefficient
-                    };
-
-                    if coefficient.is_one() {
-                        write!(f, "{witness1}*{witness2}")?;
-                    } else if (-coefficient).is_one() {
-                        write!(f, "-{witness1}*{witness2}")?;
-                    } else {
-                        write!(f, "{coefficient}*{witness1}*{witness2}")?;
-                    }
-
+                    let witnesses = [*witness1, *witness2];
+                    display_term(*coefficient, witnesses, printed_term, negate_coefficients, f)?;
                     printed_term = true;
                 }
 
@@ -218,33 +193,8 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                         continue;
                     }
 
-                    let coefficient =
-                        if negate_coefficients { -*coefficient } else { *coefficient };
-                    let coefficient_as_string = coefficient.to_string();
-                    let coefficient_is_negative = coefficient_as_string.starts_with('-');
-
-                    if printed_term {
-                        if coefficient_is_negative {
-                            write!(f, " - ")?;
-                        } else {
-                            write!(f, " + ")?;
-                        }
-                    }
-
-                    let coefficient = if printed_term && coefficient_is_negative {
-                        -coefficient
-                    } else {
-                        coefficient
-                    };
-
-                    if coefficient.is_one() {
-                        write!(f, "{witness}")?;
-                    } else if (-coefficient).is_one() {
-                        write!(f, "-{witness}")?;
-                    } else {
-                        write!(f, "{coefficient}*{witness}")?;
-                    }
-
+                    let witnesses = [*witness];
+                    display_term(*coefficient, witnesses, printed_term, negate_coefficients, f)?;
                     printed_term = true;
                 }
 
@@ -346,6 +296,46 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
     }
 }
 
+fn display_term<F: AcirField, const N: usize>(
+    coefficient: F,
+    witnesses: [Witness; N],
+    printed_term: bool,
+    negate_coefficients: bool,
+    f: &mut std::fmt::Formatter<'_>,
+) -> std::fmt::Result {
+    let coefficient = if negate_coefficients { -coefficient } else { coefficient };
+    let coefficient_as_string = coefficient.to_string();
+    let coefficient_is_negative = coefficient_as_string.starts_with('-');
+
+    if printed_term {
+        if coefficient_is_negative {
+            write!(f, " - ")?;
+        } else {
+            write!(f, " + ")?;
+        }
+    }
+
+    let coefficient =
+        if printed_term && coefficient_is_negative { -coefficient } else { coefficient };
+
+    if coefficient.is_one() {
+        // Don't print the cofficient
+    } else if (-coefficient).is_one() {
+        write!(f, "-")?;
+    } else {
+        write!(f, "{coefficient}*")?;
+    }
+
+    for (index, witness) in witnesses.iter().enumerate() {
+        if index != 0 {
+            write!(f, "*")?;
+        }
+        write!(f, "{witness}")?;
+    }
+
+    Ok(())
+}
+
 impl<F: AcirField> std::fmt::Debug for Opcode<F> {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         std::fmt::Display::fmt(self, f)

From c86a544f9250fafa8ed10d2350ddfc078dae8f8e Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Thu, 25 Sep 2025 12:16:36 -0300
Subject: [PATCH 21/25] More snapshots

---
 compiler/noirc_evaluator/src/acir/tests/call.rs | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/compiler/noirc_evaluator/src/acir/tests/call.rs b/compiler/noirc_evaluator/src/acir/tests/call.rs
index 3ce187a7dc1..e47b6fab008 100644
--- a/compiler/noirc_evaluator/src/acir/tests/call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/call.rs
@@ -154,24 +154,24 @@ fn basic_nested_call(inline_type: InlineType) {
     inputs: [w0, w1], outputs: [w2]
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w3]
-    EXPR w2 = w3
+    EXPR w3 = w2
 
     func 1
     current witness: w4
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 - w3 + 2 = 0
+    EXPR w3 = w0 + 2
     CALL func 2: PREDICATE: EXPR [ 1 ]
     inputs: [w3, w1], outputs: [w4]
-    EXPR w2 = w4
+    EXPR w4 = w2
 
     func 2
     current witness: w2
     private parameters: [w0, w1]
     public parameters: []
     return values: [w2]
-    EXPR w0 = w1
-    EXPR w0 = w2
+    EXPR w1 = w0
+    EXPR w2 = w0
     ");
 }

From b08b7707eedad93c20c77c92878cb97cd28db0ac Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Thu, 25 Sep 2025 14:06:50 -0300
Subject: [PATCH 22/25] Update acvm-repo/acir/src/circuit/opcodes.rs

Co-authored-by: Maxim Vezenov <mvezenov@gmail.com>
---
 acvm-repo/acir/src/circuit/opcodes.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index 7e81d4d02ed..94760ae5d46 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -319,7 +319,7 @@ fn display_term<F: AcirField, const N: usize>(
         if printed_term && coefficient_is_negative { -coefficient } else { coefficient };
 
     if coefficient.is_one() {
-        // Don't print the cofficient
+        // Don't print the coefficient
     } else if (-coefficient).is_one() {
         write!(f, "-")?;
     } else {

From 959add074c5c5417fe6e304be51450319c6813fc Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Thu, 25 Sep 2025 14:10:54 -0300
Subject: [PATCH 23/25] Remove extra space in test

---
 acvm-repo/acir/src/parser/tests.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 41e9488ccc7..8ee8c5d269d 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -761,7 +761,7 @@ fn assert_zero_equation() {
     private parameters: [w0, w1, w2, w2]
     public parameters: []
     return values: []
-    EXPR - w0 + w1 - 10 + 20 + w0*w2 = w2 - w3 + w0*w1 - w1*w2 - 30
+    EXPR -w0 + w1 - 10 + 20 + w0*w2 = w2 - w3 + w0*w1 - w1*w2 - 30
     ";
     let circuit = Circuit::from_str(src).unwrap();
     assert_snapshot!(circuit.to_string(), @r"

From 5e04384ce09077bb3c9873dcbc879a78c0f49026 Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Thu, 25 Sep 2025 14:25:40 -0300
Subject: [PATCH 24/25] Show expressions that equal zero as `0 = ...`

---
 acvm-repo/acir/src/circuit/mod.rs             |  2 +-
 acvm-repo/acir/src/circuit/opcodes.rs         | 24 +++++++------------
 acvm-repo/acir/src/parser/mod.rs              |  6 ++---
 acvm-repo/acir/src/parser/tests.rs            | 16 ++++++-------
 .../acvm/src/compiler/optimizers/general.rs   |  6 ++---
 .../noirc_evaluator/src/acir/tests/arrays.rs  |  2 +-
 .../src/acir/tests/brillig_call.rs            | 14 +++++------
 7 files changed, 31 insertions(+), 39 deletions(-)

diff --git a/acvm-repo/acir/src/circuit/mod.rs b/acvm-repo/acir/src/circuit/mod.rs
index 1dd1e2f8bb0..9b56183d047 100644
--- a/acvm-repo/acir/src/circuit/mod.rs
+++ b/acvm-repo/acir/src/circuit/mod.rs
@@ -544,7 +544,7 @@ mod tests {
         private parameters: []
         public parameters: [w2]
         return values: [w2]
-        EXPR 2*w1 + 8 = 0
+        EXPR 0 = 2*w1 + 8
         BLACKBOX::RANGE [w1]:8 bits []
         BLACKBOX::AND [w1, w2]:4 bits [w3]
         BLACKBOX::KECCAKF1600 [w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25] [w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43, w44, w45, w46, w47, w48, w49, w50]
diff --git a/acvm-repo/acir/src/circuit/opcodes.rs b/acvm-repo/acir/src/circuit/opcodes.rs
index 7e81d4d02ed..9fb8c487405 100644
--- a/acvm-repo/acir/src/circuit/opcodes.rs
+++ b/acvm-repo/acir/src/circuit/opcodes.rs
@@ -149,12 +149,12 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
             Opcode::AssertZero(expr) => {
                 write!(f, "EXPR ")?;
 
-                // This is set to an index if we show this expression "as an assignment", meaning
+                // This is set to an index if we show this expression "as a witness assignment", meaning
                 // that the linear combination at this index must not be printed again.
-                let mut show_as_assignment: Option<usize> = None;
+                let mut assignment_witness: Option<usize> = None;
 
                 // If true, negate all coefficients when printing.
-                // This is set to true if we show this expression "as an assignment", and the witness
+                // This is set to true if we show this expression "as a witness assignment", and the witness
                 // had a coefficient of 1 and we "moved" everything to the right of the equal sign.
                 let mut negate_coefficients = false;
 
@@ -172,9 +172,11 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                 // If we find one, show the expression as equaling this witness to everything else
                 // (this is likely to happen as in ACIR gen we tend to equate a witness to previous expressions)
                 if let Some((index, (coefficient, witness))) = linear_witness_one {
-                    show_as_assignment = Some(index);
+                    assignment_witness = Some(index);
                     negate_coefficients = coefficient.is_one();
                     write!(f, "{witness} = ")?;
+                } else {
+                    write!(f, "0 = ")?;
                 }
 
                 let mut printed_term = false;
@@ -186,7 +188,7 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                 }
 
                 for (index, (coefficient, witness)) in expr.linear_combinations.iter().enumerate() {
-                    if show_as_assignment
+                    if assignment_witness
                         .is_some_and(|show_as_assignment_index| show_as_assignment_index == index)
                     {
                         // We already printed this term as part of the assignment
@@ -199,13 +201,7 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                 }
 
                 if expr.q_c.is_zero() {
-                    if show_as_assignment.is_none() {
-                        if printed_term {
-                            write!(f, " = 0")?;
-                        } else {
-                            write!(f, "0 = 0")?;
-                        }
-                    } else if !printed_term {
+                    if !printed_term {
                         write!(f, "0")?;
                     }
                 } else {
@@ -228,10 +224,6 @@ impl<F: AcirField> std::fmt::Display for Opcode<F> {
                         coefficient
                     };
                     write!(f, "{coefficient}")?;
-
-                    if show_as_assignment.is_none() {
-                        write!(f, " = 0")?;
-                    }
                 }
 
                 Ok(())
diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index b83bfbb3858..29ab7ec6c4e 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -273,15 +273,15 @@ impl<'a> Parser<'a> {
         // Parse the right-hand side terms
         let rhs_terms = self.parse_terms_or_error()?;
 
-        // "Move" the terms to the left by negating them
-        let rhs_terms = rhs_terms.into_iter().map(|term| term.negate()).collect::<Vec<_>>();
+        // "Move" the terms to the right by negating them
+        let lhs_terms = lhs_terms.into_iter().map(|term| term.negate()).collect::<Vec<_>>();
 
         // Gather all terms, summing the constants
         let mut q_c = FieldElement::zero();
         let mut linear_combinations = Vec::new();
         let mut mul_terms = Vec::new();
 
-        for term in lhs_terms.into_iter().chain(rhs_terms) {
+        for term in rhs_terms.into_iter().chain(lhs_terms) {
             match term {
                 Term::Constant(c) => q_c += c,
                 Term::Linear(c, w) => linear_combinations.push((c, w)),
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 8ee8c5d269d..1e9834c7439 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -527,7 +527,7 @@ fn brillig_call() {
     public parameters: []
     return values: []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
-    EXPR w0*w3 - w1*w3 - 1 = 0
+    EXPR 0 = w0*w3 - w1*w3 - 1
     EXPR w2 = w0
     ";
     assert_circuit_roundtrip(src);
@@ -542,7 +542,7 @@ fn brillig_call_with_predicate() {
     return values: []
     BRILLIG CALL func 0: PREDICATE: EXPR [ 1 ]
     inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
-    EXPR w0*w3 - w1*w3 - 1 = 0
+    EXPR 0 = w0*w3 - w1*w3 - 1
     EXPR w2 = w0
     ";
     assert_circuit_roundtrip(src);
@@ -657,7 +657,7 @@ fn array_dynamic() {
     MEM (id: 3, write EXPR [ (1, w48) ] at: EXPR [ (1, w38) ])
     MEM (id: 3, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w49) ])
     MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w50) ])
-    EXPR -w31*w36 = 0
+    EXPR 0 = -w31*w36
     EXPR w51 = w21*w31
     MEM (id: 0, read at: EXPR [ (1, w51) ], value: EXPR [ (1, w52) ])
     EXPR w53 = -w31*w52 + w52
@@ -665,7 +665,7 @@ fn array_dynamic() {
     MEM (id: 0, read at: EXPR [ (1, w46) ], value: EXPR [ (1, w54) ])
     EXPR w55 = -w31 + 1
     EXPR w56 = -w31*w49 + w31*w50 + w49
-    EXPR w31*w54 + w55*w56 - 109 = 0
+    EXPR 0 = w31*w54 + w55*w56 - 109
     EXPR w57 = 246
     EXPR w58 = 159
     EXPR w59 = 32
@@ -678,7 +678,7 @@ fn array_dynamic() {
     MEM (id: 4, read at: EXPR [ (1, w10) ], value: EXPR [ (1, w65) ])
     MEM (id: 4, read at: EXPR [ (1, w11) ], value: EXPR [ (1, w66) ])
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w62) (1, w63) (1, w64) (1, w65) (1, w66) ]], outputs: [w67]
-    EXPR w62*w67 + w63*w67 + w64*w67 + w65*w67 + w66*w67 - 1 = 0
+    EXPR 0 = w62*w67 + w63*w67 + w64*w67 + w65*w67 + w66*w67 - 1
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w18) ], EXPR [ 4294967296 ]], outputs: [w68, w69]
     BLACKBOX::RANGE [w68]:222 bits []
     BLACKBOX::RANGE [w69]:32 bits []
@@ -687,7 +687,7 @@ fn array_dynamic() {
     BLACKBOX::RANGE [w70]:222 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (-1, w68) 5096253676302562286669017222071363378443840053029366383258766538131 ]], outputs: [w71]
     EXPR w72 = w68*w71 - 5096253676302562286669017222071363378443840053029366383258766538131*w71 + 1
-    EXPR -w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72 = 0
+    EXPR 0 = -w68*w72 + 5096253676302562286669017222071363378443840053029366383258766538131*w72
     EXPR w73 = w69*w72 + 268435455*w72
     BLACKBOX::RANGE [w73]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (-1, w69) 4294967299 ], EXPR [ 4294967296 ]], outputs: [w74, w75]
@@ -720,7 +720,7 @@ fn fold_basic() {
     public parameters: []
     return values: [w2]
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) (-1, w1) ]], outputs: [w3]
-    EXPR w0*w3 - w1*w3 - 1 = 0
+    EXPR 0 = w0*w3 - w1*w3 - 1
     EXPR w2 = w0
     ";
     assert_program_roundtrip(src);
@@ -769,6 +769,6 @@ fn assert_zero_equation() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    EXPR w3 = -w0*w2 + w0*w1 - w1*w2 + w0 - w1 + w2 - 40
+    EXPR w3 = w0*w1 - w1*w2 - w0*w2 + w2 + w0 - w1 - 40
     ");
 }
diff --git a/acvm-repo/acvm/src/compiler/optimizers/general.rs b/acvm-repo/acvm/src/compiler/optimizers/general.rs
index 4a8d3dbc9d1..45a458c7e53 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/general.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/general.rs
@@ -102,7 +102,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR w0*w1 = 0
+        EXPR 0 = -w0*w1
         ");
     }
 
@@ -147,7 +147,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 9*w0*w1 = 0
+        EXPR 0 = -9*w0*w1
         ");
     }
 
@@ -190,7 +190,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 6*w0 = 0
+        EXPR 0 = -6*w0
         ");
     }
 
diff --git a/compiler/noirc_evaluator/src/acir/tests/arrays.rs b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
index 231db2fb085..2b235dcb579 100644
--- a/compiler/noirc_evaluator/src/acir/tests/arrays.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/arrays.rs
@@ -237,7 +237,7 @@ fn zero_length_array_constant() {
     private parameters: []
     public parameters: []
     return values: []
-    EXPR 1 = 0
+    EXPR 0 = 1
     ");
 }
 
diff --git a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
index 8a7dd222bac..719ff18a90b 100644
--- a/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
+++ b/compiler/noirc_evaluator/src/acir/tests/brillig_call.rs
@@ -153,7 +153,7 @@ fn multiple_brillig_stdlib_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
-    EXPR w1*w3 - 1 = 0
+    EXPR 0 = w1*w3 - 1
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
@@ -162,7 +162,7 @@ fn multiple_brillig_stdlib_calls() {
     EXPR w5 = -w1*w4 + w0
     EXPR w4 = w2
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w2) ]], outputs: [w7]
-    EXPR w2*w7 - 1 = 0
+    EXPR 0 = w2*w7 - 1
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w8, w9]
     BLACKBOX::RANGE [w9]:32 bits []
     EXPR w10 = w2 - w9 - 1
@@ -241,7 +241,7 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
-    EXPR w1*w3 - 1 = 0
+    EXPR 0 = w1*w3 - 1
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
@@ -254,7 +254,7 @@ fn brillig_stdlib_calls_with_regular_brillig_call() {
     BRILLIG CALL func 0: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w8]
     BLACKBOX::RANGE [w8]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) ]], outputs: [w9]
-    EXPR w2*w9 - 1 = 0
+    EXPR 0 = w2*w9 - 1
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w10, w11]
     BLACKBOX::RANGE [w11]:32 bits []
     EXPR w12 = w2 - w11 - 1
@@ -375,7 +375,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     BLACKBOX::RANGE [w1]:32 bits []
     BLACKBOX::RANGE [w2]:32 bits []
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w1) ]], outputs: [w3]
-    EXPR w1*w3 - 1 = 0
+    EXPR 0 = w1*w3 - 1
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w0) ], EXPR [ (1, w1) ]], outputs: [w4, w5]
     BLACKBOX::RANGE [w4]:32 bits []
     BLACKBOX::RANGE [w5]:32 bits []
@@ -390,7 +390,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     CALL func 1: PREDICATE: EXPR [ 1 ]
     inputs: [w0, w1], outputs: [w9]
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w2) ]], outputs: [w10]
-    EXPR w2*w10 - 1 = 0
+    EXPR 0 = w2*w10 - 1
     BRILLIG CALL func 2: inputs: [EXPR [ (1, w1) ], EXPR [ (1, w2) ]], outputs: [w11, w12]
     BLACKBOX::RANGE [w12]:32 bits []
     EXPR w13 = w2 - w12 - 1
@@ -408,7 +408,7 @@ fn brillig_stdlib_calls_with_multiple_acir_calls() {
     EXPR w3 = w0 - w1
     BRILLIG CALL func 1: inputs: [EXPR [ (1, w3) ]], outputs: [w4]
     EXPR w5 = -w3*w4 + 1
-    EXPR w3*w5 = 0
+    EXPR 0 = w3*w5
     EXPR w5 = 0
     EXPR w2 = w0
 

From ecfb272712388ecbec34a18c0e95e4f39056d344 Mon Sep 17 00:00:00 2001
From: Ary Borenszweig <asterite@gmail.com>
Date: Thu, 25 Sep 2025 14:36:03 -0300
Subject: [PATCH 25/25] Preserve original signs when it's a zero equality

---
 acvm-repo/acir/src/parser/mod.rs              | 50 +++++++++++++------
 acvm-repo/acir/src/parser/tests.rs            | 21 +++++++-
 .../acvm/src/compiler/optimizers/general.rs   |  6 +--
 3 files changed, 57 insertions(+), 20 deletions(-)

diff --git a/acvm-repo/acir/src/parser/mod.rs b/acvm-repo/acir/src/parser/mod.rs
index 29ab7ec6c4e..a9e0667488d 100644
--- a/acvm-repo/acir/src/parser/mod.rs
+++ b/acvm-repo/acir/src/parser/mod.rs
@@ -273,23 +273,20 @@ impl<'a> Parser<'a> {
         // Parse the right-hand side terms
         let rhs_terms = self.parse_terms_or_error()?;
 
-        // "Move" the terms to the right by negating them
-        let lhs_terms = lhs_terms.into_iter().map(|term| term.negate()).collect::<Vec<_>>();
-
-        // Gather all terms, summing the constants
-        let mut q_c = FieldElement::zero();
-        let mut linear_combinations = Vec::new();
-        let mut mul_terms = Vec::new();
-
-        for term in rhs_terms.into_iter().chain(lhs_terms) {
-            match term {
-                Term::Constant(c) => q_c += c,
-                Term::Linear(c, w) => linear_combinations.push((c, w)),
-                Term::Multiplication(c, w1, w2) => mul_terms.push((c, w1, w2)),
-            }
-        }
+        // If we have something like `0 = ...` or `... = 0`, just consider the expressions
+        // on the non-zero side. Otherwise we could be "moving" terms to the other side and
+        // negating them, which won't accurately reflect the original expression.
+        let expression = if is_zero_term(&lhs_terms) {
+            build_expression_from_terms(rhs_terms.into_iter())
+        } else if is_zero_term(&rhs_terms) {
+            build_expression_from_terms(lhs_terms.into_iter())
+        } else {
+            // "Move" the terms to the left by negating them
+            let rhs_terms = rhs_terms.into_iter().map(|term| term.negate()).collect::<Vec<_>>();
+            build_expression_from_terms(lhs_terms.into_iter().chain(rhs_terms))
+        };
 
-        Ok(Expression { mul_terms, linear_combinations, q_c })
+        Ok(expression)
     }
 
     fn parse_terms_or_error(&mut self) -> ParseResult<Vec<Term>> {
@@ -1083,6 +1080,27 @@ impl<'a> Parser<'a> {
     }
 }
 
+fn build_expression_from_terms(terms: impl Iterator<Item = Term>) -> Expression<FieldElement> {
+    // Gather all terms, summing the constants
+    let mut q_c = FieldElement::zero();
+    let mut linear_combinations = Vec::new();
+    let mut mul_terms = Vec::new();
+
+    for term in terms {
+        match term {
+            Term::Constant(c) => q_c += c,
+            Term::Linear(c, w) => linear_combinations.push((c, w)),
+            Term::Multiplication(c, w1, w2) => mul_terms.push((c, w1, w2)),
+        }
+    }
+
+    Expression { mul_terms, linear_combinations, q_c }
+}
+
+fn is_zero_term(terms: &[Term]) -> bool {
+    terms.len() == 1 && matches!(terms[0], Term::Constant(c) if c.is_zero())
+}
+
 fn eof_spanned_token() -> SpannedToken {
     SpannedToken::new(Token::Eof, Default::default())
 }
diff --git a/acvm-repo/acir/src/parser/tests.rs b/acvm-repo/acir/src/parser/tests.rs
index 1e9834c7439..98b0e418dea 100644
--- a/acvm-repo/acir/src/parser/tests.rs
+++ b/acvm-repo/acir/src/parser/tests.rs
@@ -769,6 +769,25 @@ fn assert_zero_equation() {
     private parameters: [w0, w1, w2]
     public parameters: []
     return values: []
-    EXPR w3 = w0*w1 - w1*w2 - w0*w2 + w2 + w0 - w1 - 40
+    EXPR w3 = -w0*w2 + w0*w1 - w1*w2 + w0 - w1 + w2 - 40
+    ");
+}
+
+#[test]
+fn does_not_negate_when_equal_to_zero() {
+    let src = "
+    current witness: w9
+    private parameters: [w0, w1, w2]
+    public parameters: []
+    return values: []
+    EXPR w0*w1 + w0*w2 = 0
+    ";
+    let circuit = Circuit::from_str(src).unwrap();
+    assert_snapshot!(circuit.to_string(), @r"
+    current witness: w9
+    private parameters: [w0, w1, w2]
+    public parameters: []
+    return values: []
+    EXPR 0 = w0*w1 + w0*w2
     ");
 }
diff --git a/acvm-repo/acvm/src/compiler/optimizers/general.rs b/acvm-repo/acvm/src/compiler/optimizers/general.rs
index 45a458c7e53..788981b33af 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/general.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/general.rs
@@ -102,7 +102,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 0 = -w0*w1
+        EXPR 0 = w0*w1
         ");
     }
 
@@ -147,7 +147,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 0 = -9*w0*w1
+        EXPR 0 = 9*w0*w1
         ");
     }
 
@@ -190,7 +190,7 @@ mod tests {
         private parameters: [w0, w1]
         public parameters: []
         return values: []
-        EXPR 0 = -6*w0
+        EXPR 0 = 6*w0
         ");
     }