diff --git a/compiler/noirc_evaluator/src/ssa/interpreter/errors.rs b/compiler/noirc_evaluator/src/ssa/interpreter/errors.rs
index 43562103603..4c81179718b 100644
--- a/compiler/noirc_evaluator/src/ssa/interpreter/errors.rs
+++ b/compiler/noirc_evaluator/src/ssa/interpreter/errors.rs
@@ -14,10 +14,10 @@ pub enum InterpreterError {
     /// These errors are all the result from malformed input SSA
     #[error("{0}")]
     Internal(InternalError),
-    #[error("constrain {lhs_id} == {rhs_id} failed:\n    {lhs} != {rhs}")]
-    ConstrainEqFailed { lhs: String, lhs_id: ValueId, rhs: String, rhs_id: ValueId },
-    #[error("constrain {lhs_id} != {rhs_id} failed:\n    {lhs} == {rhs}")]
-    ConstrainNeFailed { lhs: String, lhs_id: ValueId, rhs: String, rhs_id: ValueId },
+    #[error("constrain {lhs_id} == {rhs_id}{msg} failed:\n    {lhs} != {rhs}")]
+    ConstrainEqFailed { lhs: String, lhs_id: ValueId, rhs: String, rhs_id: ValueId, msg: String },
+    #[error("constrain {lhs_id} != {rhs_id}{msg} failed:\n    {lhs} == {rhs}")]
+    ConstrainNeFailed { lhs: String, lhs_id: ValueId, rhs: String, rhs_id: ValueId, msg: String },
     #[error("static_assert `{condition}` failed: {message}")]
     StaticAssertFailed { condition: ValueId, message: String },
     #[error(
diff --git a/compiler/noirc_evaluator/src/ssa/interpreter/mod.rs b/compiler/noirc_evaluator/src/ssa/interpreter/mod.rs
index 187636dde60..9959a3473ee 100644
--- a/compiler/noirc_evaluator/src/ssa/interpreter/mod.rs
+++ b/compiler/noirc_evaluator/src/ssa/interpreter/mod.rs
@@ -5,7 +5,9 @@ use super::{
     ir::{
         dfg::DataFlowGraph,
         function::{Function, FunctionId, RuntimeType},
-        instruction::{ArrayOffset, Binary, BinaryOp, Instruction, TerminatorInstruction},
+        instruction::{
+            ArrayOffset, Binary, BinaryOp, ConstrainError, Instruction, TerminatorInstruction,
+        },
         types::Type,
         value::ValueId,
     },
@@ -413,7 +415,18 @@ impl<'ssa> Interpreter<'ssa> {
                     let rhs = rhs.to_string();
                     let lhs_id = *lhs_id;
                     let rhs_id = *rhs_id;
-                    return Err(InterpreterError::ConstrainEqFailed { lhs, lhs_id, rhs, rhs_id });
+                    let msg = if let Some(ConstrainError::StaticString(msg)) = constrain_error {
+                        format!(", \"{msg}\"")
+                    } else {
+                        "".to_string()
+                    };
+                    return Err(InterpreterError::ConstrainEqFailed {
+                        lhs,
+                        lhs_id,
+                        rhs,
+                        rhs_id,
+                        msg,
+                    });
                 }
                 Ok(())
             }
@@ -425,7 +438,18 @@ impl<'ssa> Interpreter<'ssa> {
                     let rhs = rhs.to_string();
                     let lhs_id = *lhs_id;
                     let rhs_id = *rhs_id;
-                    return Err(InterpreterError::ConstrainNeFailed { lhs, lhs_id, rhs, rhs_id });
+                    let msg = if let Some(ConstrainError::StaticString(msg)) = constrain_error {
+                        format!(", \"{msg}\"")
+                    } else {
+                        "".to_string()
+                    };
+                    return Err(InterpreterError::ConstrainNeFailed {
+                        lhs,
+                        lhs_id,
+                        rhs,
+                        rhs_id,
+                        msg,
+                    });
                 }
                 Ok(())
             }
diff --git a/compiler/noirc_frontend/src/monomorphization/printer.rs b/compiler/noirc_frontend/src/monomorphization/printer.rs
index 3f2067d0340..8e4d877f864 100644
--- a/compiler/noirc_frontend/src/monomorphization/printer.rs
+++ b/compiler/noirc_frontend/src/monomorphization/printer.rs
@@ -183,9 +183,15 @@ impl AstPrinter {
                 )?;
                 self.print_expr(&let_expr.expression, f)
             }
-            Expression::Constrain(expr, ..) => {
-                write!(f, "constrain ")?;
-                self.print_expr(expr, f)
+            Expression::Constrain(expr, _, payload) => {
+                write!(f, "assert(")?;
+                self.print_expr(expr, f)?;
+                if let Some(payload) = payload {
+                    write!(f, ", ")?;
+                    self.print_expr(&payload.as_ref().0, f)?;
+                }
+                write!(f, ")")?;
+                Ok(())
             }
             Expression::Assign(assign) => {
                 self.print_lvalue(&assign.lvalue, f)?;
diff --git a/compiler/noirc_frontend/src/ownership/tests.rs b/compiler/noirc_frontend/src/ownership/tests.rs
index 1ba46e81053..8ba497404f5 100644
--- a/compiler/noirc_frontend/src/ownership/tests.rs
+++ b/compiler/noirc_frontend/src/ownership/tests.rs
@@ -33,10 +33,10 @@ fn last_use_in_if_branches() {
     unconstrained fn main$f0(d$l0: [Field; 2]) -> () {
         if (len$f1(d$l0.clone()) == 2) {
             if (len$f1(d$l0.clone()) == 2) {
-                constrain eq$f2(d$l0, [5, 6]);
+                assert(eq$f2(d$l0, [5, 6]));
             }
         } else {
-            constrain eq$f2(d$l0, [5, 6]);
+            assert(eq$f2(d$l0, [5, 6]));
         }
     }
     unconstrained fn len$f1(arr$l1: [Field; 2]) -> u32 {
diff --git a/tooling/ast_fuzzer/fuzz/src/targets/comptime_vs_brillig.rs b/tooling/ast_fuzzer/fuzz/src/targets/comptime_vs_brillig.rs
index 552d8c39d0a..e21d56f17ec 100644
--- a/tooling/ast_fuzzer/fuzz/src/targets/comptime_vs_brillig.rs
+++ b/tooling/ast_fuzzer/fuzz/src/targets/comptime_vs_brillig.rs
@@ -14,6 +14,7 @@ use noir_ast_fuzzer::rewrite::change_all_functions_into_unconstrained;
 pub fn fuzz(u: &mut Unstructured) -> eyre::Result<()> {
     let config = Config {
         // We created enough bug tickets due to overflows
+        // TODO(#8817): Comptime code fails to compile if there is an overflow, which causes a panic.
         avoid_overflow: true,
         // also with negative values
         avoid_negative_int_literals: true,
@@ -23,6 +24,8 @@ pub fn fuzz(u: &mut Unstructured) -> eyre::Result<()> {
         avoid_large_int_literals: true,
         // Avoid break/continue
         avoid_loop_control: true,
+        // TODO(#8817): Comptime code fails to compile if there is an assertion failure, which causes a panic.
+        avoid_constrain: true,
         // Has to only use expressions valid in comptime
         comptime_friendly: true,
         // Force brillig
diff --git a/tooling/ast_fuzzer/fuzz/src/targets/orig_vs_morph.rs b/tooling/ast_fuzzer/fuzz/src/targets/orig_vs_morph.rs
index 71199df03a3..7ff4f71015c 100644
--- a/tooling/ast_fuzzer/fuzz/src/targets/orig_vs_morph.rs
+++ b/tooling/ast_fuzzer/fuzz/src/targets/orig_vs_morph.rs
@@ -1,16 +1,16 @@
 //! Perform random equivalence mutations on the AST and check that the
 //! execution result does not change, a.k.a. metamorphic testing.
 
-use std::collections::{HashSet, VecDeque};
-
 use crate::{compare_results_compiled, create_ssa_or_die, default_ssa_options};
 use arbitrary::{Arbitrary, Unstructured};
 use color_eyre::eyre;
 use noir_ast_fuzzer::compare::{CompareMorph, CompareOptions};
+use noir_ast_fuzzer::visitor;
 use noir_ast_fuzzer::{Config, visitor::visit_expr_mut};
-use noir_ast_fuzzer::{expr, visitor};
 use noirc_frontend::ast::UnaryOp;
-use noirc_frontend::monomorphization::ast::{Expression, FuncId, Function, Program, Unary};
+use noirc_frontend::monomorphization::ast::{
+    Call, Definition, Expression, Function, Ident, Program, Unary,
+};
 
 pub fn fuzz(u: &mut Unstructured) -> eyre::Result<()> {
     let rules = rules::all();
@@ -42,9 +42,8 @@ fn rewrite_program(
     rules: &[rules::Rule],
     max_rewrites: usize,
 ) {
-    let reachable = reachable_functions(program);
     for func in program.functions.iter_mut() {
-        if func.name.ends_with("_proxy") || !reachable.contains(&func.id) {
+        if func.name.ends_with("_proxy") {
             continue;
         }
         rewrite_function(u, func, rules, max_rewrites);
@@ -92,9 +91,11 @@ impl MorphContext<'_> {
             }
             match expr {
                 Expression::For(for_) => {
+                    // Separate context for just the ranges.
                     let range_ctx = rules::Context { is_in_range: true, ..*ctx };
                     self.rewrite_expr(&range_ctx, u, &mut for_.start_range);
                     self.rewrite_expr(&range_ctx, u, &mut for_.end_range);
+                    // Original context for the body.
                     self.rewrite_expr(ctx, u, &mut for_.block);
                     // No need to visit children, we just visited them.
                     false
@@ -106,6 +107,14 @@ impl MorphContext<'_> {
                     self.rewrite_expr(&ctx, u, &mut unary.rhs);
                     false
                 }
+                Expression::Call(call) if is_special_call(call) => {
+                    let ctx = rules::Context { is_in_special_call: true, ..*ctx };
+                    for arg in call.arguments.iter_mut() {
+                        self.rewrite_expr(&ctx, u, arg);
+                    }
+                    false
+                }
+                // The rest can just have the rules applied on them, using the same context.
                 _ => {
                     for rule in self.rules {
                         match self.try_apply_rule(ctx, u, expr, rule) {
@@ -174,29 +183,15 @@ fn estimate_applicable_rules(
     count
 }
 
-/// Collect the functions reachable from `main`.
-///
-/// We don't want to waste our time morphing functions that won't be called.
-///
-/// It would be nice if they were removed during AST generation, but if we
-/// remove an item from `Programs::functions`, the calls made to them would
-/// need to be updated according to their new position in the vector.
-fn reachable_functions(program: &Program) -> HashSet<FuncId> {
-    let mut reachable = HashSet::new();
-    let mut queue = VecDeque::new();
-
-    queue.push_back(Program::main_id());
-
-    while let Some(func_id) = queue.pop_front() {
-        if !reachable.insert(func_id) {
-            continue;
-        }
-        let func = &program.functions[func_id.0 as usize];
-        let callees = expr::callees(&func.body);
-        queue.extend(callees);
-    }
-
-    reachable
+/// Check if we are calling an oracle or builtin function.
+fn is_special_call(call: &Call) -> bool {
+    matches!(
+        call.func.as_ref(),
+        Expression::Ident(Ident {
+            definition: Definition::Oracle(_) | Definition::Builtin(_) | Definition::LowLevel(_),
+            ..
+        })
+    )
 }
 
 /// Metamorphic transformation rules.
@@ -212,10 +207,12 @@ mod rules {
     pub struct Context {
         /// Is the function we're rewriting unconstrained?
         pub unconstrained: bool,
-        /// Are we rewriting an expression which is a range of a `for` loop?
+        /// Are we rewriting an expression which is a `start` or `end` of a `for` loop?
         pub is_in_range: bool,
         /// Are we in an expression that we're just taking a mutable reference to?
         pub is_in_ref_mut: bool,
+        /// Are we processing the arguments of an non-user function call, such as an oracle or built-in?
+        pub is_in_special_call: bool,
     }
 
     /// Check if the rule can be applied on an expression.
@@ -301,6 +298,11 @@ mod rules {
         if ctx.is_in_ref_mut {
             return false;
         }
+        // We don't want to mess with the arguments of a `println`, because the printer assumes they are bool literals.
+        // Similarly a `constrain` call is expected to have a single boolean expression.
+        if ctx.is_in_special_call {
+            return false;
+        }
         // We can apply boolean rule on anything that returns a bool,
         // unless the expression can have a side effect, which we don't want to duplicate.
         if let Some(typ) = expr.return_type() {
diff --git a/tooling/ast_fuzzer/src/compare/interpreted.rs b/tooling/ast_fuzzer/src/compare/interpreted.rs
index ebb474d8a1b..6f6c57fd7d7 100644
--- a/tooling/ast_fuzzer/src/compare/interpreted.rs
+++ b/tooling/ast_fuzzer/src/compare/interpreted.rs
@@ -134,6 +134,21 @@ impl Comparable for ssa::interpreter::errors::InterpreterError {
                 }
                 details_or_sanitize(i1) == details_or_sanitize(i2)
             }
+            (
+                ConstrainEqFailed { lhs: _lhs1, rhs: _rhs1, msg: msg1, .. },
+                ConstrainEqFailed { lhs: _lhs2, rhs: _rhs2, msg: msg2, .. },
+            )
+            | (
+                ConstrainNeFailed { lhs: _lhs1, rhs: _rhs1, msg: msg1, .. },
+                ConstrainNeFailed { lhs: _lhs2, rhs: _rhs2, msg: msg2, .. },
+            ) => {
+                // The sides might be flipped: `u1 0 == u1 1` vs `u1 1 == u1 0`.
+                // Unfortunately we often see the type change as well, which makes it more difficult to compare,
+                // for example `Field 313339671284855045676773137498590239475 != Field 0` vs `u128 313339671284855045676773137498590239475 != u128 0`,
+                // or `i64 -1615928006 != i64 -5568658583620095790` vs `u64 18446744072093623610 != u64 12878085490089455826`
+                // (lhs1 == lhs2 && rhs1 == rhs2 || lhs1 == rhs2 && rhs1 == lhs2) && msg1 == msg2
+                msg1 == msg2
+            }
             (e1, e2) => {
                 // The format strings contain SSA instructions,
                 // where the only difference might be the value ID.
diff --git a/tooling/ast_fuzzer/src/compare/mod.rs b/tooling/ast_fuzzer/src/compare/mod.rs
index 88a7d2fca28..fc6584580b1 100644
--- a/tooling/ast_fuzzer/src/compare/mod.rs
+++ b/tooling/ast_fuzzer/src/compare/mod.rs
@@ -108,7 +108,7 @@ where
                     // Both programs failed the same way.
                     Ok(None)
                 } else {
-                    bail!("both programs failed: {e1} vs {e2}\n{e1:?}\n{e2:?}")
+                    bail!("both programs failed:\n{e1}\n!=\n{e2}\n\n{e1:?}\n{e2:?}")
                 }
             }
             CompareResult::LeftFailed(e, _) => {
diff --git a/tooling/ast_fuzzer/src/lib.rs b/tooling/ast_fuzzer/src/lib.rs
index 489869731b4..b10c2220c0c 100644
--- a/tooling/ast_fuzzer/src/lib.rs
+++ b/tooling/ast_fuzzer/src/lib.rs
@@ -63,6 +63,8 @@ pub struct Config {
     pub avoid_loop_control: bool,
     /// Avoid using function pointers in parameters.
     pub avoid_lambdas: bool,
+    /// Avoid using constrain statements.
+    pub avoid_constrain: bool,
     /// Only use comptime friendly expressions.
     pub comptime_friendly: bool,
 }
@@ -85,6 +87,7 @@ impl Default for Config {
             ("for", 22),
             ("let", 25),
             ("call", 5),
+            ("constrain", 5),
         ]);
         let stmt_freqs_brillig = Freqs::new(&[
             ("drop", 0),
@@ -98,6 +101,7 @@ impl Default for Config {
             ("let", 20),
             ("call", 5),
             ("print", 15),
+            ("constrain", 10),
         ]);
         Self {
             max_globals: 3,
@@ -122,6 +126,7 @@ impl Default for Config {
             avoid_negative_int_literals: false,
             avoid_loop_control: false,
             avoid_lambdas: false,
+            avoid_constrain: false,
             comptime_friendly: false,
         }
     }
diff --git a/tooling/ast_fuzzer/src/program/func.rs b/tooling/ast_fuzzer/src/program/func.rs
index 251f2ae73df..c4f9433a6d9 100644
--- a/tooling/ast_fuzzer/src/program/func.rs
+++ b/tooling/ast_fuzzer/src/program/func.rs
@@ -30,6 +30,9 @@ use super::{
     types,
 };
 
+/// Use random strings to identify constraints.
+const CONSTRAIN_MSG_TYPE: Type = Type::String(3);
+
 /// Something akin to a forward declaration of a function, capturing the details required to:
 /// 1. call the function from the other function bodies
 /// 2. generate the final HIR function signature
@@ -693,7 +696,6 @@ impl<'a> FunctionContext<'a> {
             Freq::new(u, &self.ctx.config.stmt_freqs_acir)?
         };
         // TODO(#7926): Match
-        // TODO(#7932): Constrain
 
         // Start with `drop`, it doesn't need to be frequent even if others are disabled.
         if freq.enabled("drop") {
@@ -702,6 +704,13 @@ impl<'a> FunctionContext<'a> {
             }
         }
 
+        // We don't want constraints to get too frequent, as it could dominate all outcome.
+        if freq.enabled_when("constrain", !self.ctx.config.avoid_constrain) {
+            if let Some(e) = self.gen_constrain(u)? {
+                return Ok(e);
+            }
+        }
+
         // Require a positive budget, so that we have some for the block itself and its contents.
         if freq.enabled_when("if", self.budget > 1) {
             return self.gen_if(u, &Type::Unit, self.max_depth(), Flags::TOP);
@@ -906,6 +915,25 @@ impl<'a> FunctionContext<'a> {
         Ok(Some(call))
     }
 
+    /// Generate a `constrain` statement, if there is some local variable we can do it on.
+    ///
+    /// Arbitrary constraints are very likely to fail, so we don't want too many of them,
+    /// otherwise they might mask disagreements in return values.
+    fn gen_constrain(&mut self, u: &mut Unstructured) -> arbitrary::Result<Option<Expression>> {
+        // Generate a condition that evaluates to bool.
+        let Some(cond) = self.gen_binary(u, &Type::Bool, self.max_depth())? else {
+            return Ok(None);
+        };
+        // Generate a unique message for the assertion, so it's easy to find which one failed.
+        let msg = expr::gen_literal(u, &CONSTRAIN_MSG_TYPE)?;
+        let cons = Expression::Constrain(
+            Box::new(cond),
+            Location::dummy(),
+            Some(Box::new((msg, types::to_hir_type(&CONSTRAIN_MSG_TYPE)))),
+        );
+        Ok(Some(cons))
+    }
+
     /// Generate an if-then-else statement or expression.
     fn gen_if(
         &mut self,
diff --git a/tooling/ast_fuzzer/tests/calibration.rs b/tooling/ast_fuzzer/tests/calibration.rs
index 832aebb7b4c..58d3c363c94 100644
--- a/tooling/ast_fuzzer/tests/calibration.rs
+++ b/tooling/ast_fuzzer/tests/calibration.rs
@@ -8,7 +8,7 @@
 //! ```shell
 //! cargo test -p noir_ast_fuzzer --test calibration -- --nocapture
 //! ```
-use std::collections::BTreeMap;
+use std::{collections::BTreeMap, ops::RangeInclusive};
 
 use arbtest::arbtest;
 use noir_ast_fuzzer::{Config, arb_program, visitor::visit_expr};
@@ -67,6 +67,13 @@ fn arb_program_freqs_in_expected_range() {
         keys.iter().map(|key| counts[&unconstrained][group][key] * 100 / total).sum::<usize>()
     };
 
+    let assert_both = |group: &str, key: &str, range: RangeInclusive<usize>| {
+        let a = freq_100(false, group, &[key]);
+        let b = freq_100(true, group, &[key]);
+        assert!(range.contains(&a), "ACIR {group}/{key} should be in {range:?}: {a}");
+        assert!(range.contains(&b), "Brillig {group}/{key} should be in {range:?}: {b}");
+    };
+
     // Assert relative frequencies
     let loops_a = freq_100(false, "stmt", &["for"]);
     let loops_b = freq_100(true, "stmt", &["for", "loop", "while"]);
@@ -76,6 +83,8 @@ fn arb_program_freqs_in_expected_range() {
     assert!(loop_range.contains(&loops_a), "ACIR loops should be ~10: {loops_a}");
     assert!(loop_range.contains(&loops_b), "Brillig loops should be ~10: {loops_b}");
     assert!(break_b >= loops_b, "Brillig should break out of loops: {break_b} >= {loops_b}");
+
+    assert_both("stmt", "constrain", 1..=3);
 }
 
 /// Classify the expression into "expr" or "stmt" for frequency settings.