diff --git a/compiler/noirc_evaluator/src/ssa.rs b/compiler/noirc_evaluator/src/ssa.rs
index 41251b8865d..12cb375d968 100644
--- a/compiler/noirc_evaluator/src/ssa.rs
+++ b/compiler/noirc_evaluator/src/ssa.rs
@@ -207,6 +207,7 @@ pub fn primary_passes(options: &SsaEvaluatorOptions) -> Vec<SsaPass> {
         // We can safely place the pass before DIE as that pass only removes instructions.
         // We also need DIE's tracking of used globals in case the array get transformations
         // end up using an existing constant from the globals space.
+        SsaPass::new(Ssa::arithmetic_optimization, "Arithmetic Optimizations"),
         // This pass might result in otherwise unused global constant becoming used,
         // because the creation of shifted index constants can reuse their IDs.
         SsaPass::new(Ssa::brillig_array_get_and_set, "Brillig Array Get and Set Optimizations"),
diff --git a/compiler/noirc_evaluator/src/ssa/opt/arithmetic.rs b/compiler/noirc_evaluator/src/ssa/opt/arithmetic.rs
new file mode 100644
index 00000000000..213b11f9d5c
--- /dev/null
+++ b/compiler/noirc_evaluator/src/ssa/opt/arithmetic.rs
@@ -0,0 +1,277 @@
+use std::collections::VecDeque;
+
+use acvm::{AcirField, FieldElement};
+use fxhash::FxHashSet as HashSet;
+use iter_extended::vecmap;
+
+use crate::ssa::{
+    ir::{
+        basic_block::BasicBlockId,
+        dfg::{DataFlowGraph, InsertInstructionResult, simplify::SimplifyResult},
+        function::Function,
+        instruction::{
+            Binary, BinaryOp, Instruction, InstructionId, binary::eval_constant_binary_op,
+        },
+        types::NumericType,
+        value::{Value, ValueId},
+    },
+    ssa_gen::Ssa,
+};
+
+impl Ssa {
+    /// Map arrays with the last instruction that uses it
+    /// For this we simply process all the instructions in execution order
+    /// and update the map whenever there is a match
+    #[tracing::instrument(level = "trace", skip(self))]
+    pub(crate) fn arithmetic_optimization(mut self) -> Self {
+        for func in self.functions.values_mut() {
+            func.arithmetic_optimization();
+        }
+        self
+    }
+}
+
+impl Function {
+    pub(crate) fn arithmetic_optimization(&mut self) {
+        let mut context = Context::new();
+        context.block_queue.push_back(self.entry_block());
+
+        while let Some(block) = context.block_queue.pop_front() {
+            if context.visited_blocks.contains(&block) {
+                continue;
+            }
+
+            context.visited_blocks.insert(block);
+            context.optimize_arithmetic_in_block(self, block);
+        }
+    }
+}
+
+struct Context {
+    /// Maps pre-folded ValueIds to the new ValueIds obtained by re-inserting the instruction.
+    visited_blocks: HashSet<BasicBlockId>,
+    block_queue: VecDeque<BasicBlockId>,
+}
+
+impl Context {
+    fn new() -> Self {
+        Self { visited_blocks: Default::default(), block_queue: Default::default() }
+    }
+
+    fn optimize_arithmetic_in_block(&mut self, function: &mut Function, block_id: BasicBlockId) {
+        let instructions = function.dfg[block_id].take_instructions();
+
+        for instruction_id in instructions {
+            self.fold_constants_into_instruction(function, block_id, instruction_id);
+        }
+
+        // Map a terminator in place, replacing any ValueId in the terminator with the
+        // resolved version of that value id from the simplification cache's internal value mapping.
+        let mut terminator = function.dfg[block_id].take_terminator();
+        terminator.map_values_mut(|value| function.dfg.resolve(value));
+        function.dfg[block_id].set_terminator(terminator);
+
+        self.block_queue.extend(function.dfg[block_id].successors());
+    }
+
+    fn fold_constants_into_instruction(
+        &mut self,
+        function: &mut Function,
+        block: BasicBlockId,
+        id: InstructionId,
+    ) {
+        let instruction = function.dfg[id].clone();
+        let old_results = function.dfg.instruction_results(id).to_vec();
+        let ctrl_typevars = instruction
+            .requires_ctrl_typevars()
+            .then(|| vecmap(&old_results, |result| function.dfg.type_of_value(*result)));
+
+        let new_instruction = match instruction {
+            Instruction::Binary(binary) => {
+                let binary = simplify_binary(binary.clone(), &mut function.dfg);
+                match simplify_using_previous_instruction(&binary, &mut function.dfg) {
+                    SimplifyResult::SimplifiedToInstruction(instruction) => instruction,
+                    SimplifyResult::None => Instruction::Binary(binary),
+                    _ => unreachable!("we're doing bad things"),
+                }
+            }
+            _ => instruction,
+        };
+
+        let call_stack = function.dfg.get_instruction_call_stack_id(id);
+
+        let new_results = match function.dfg.insert_instruction_and_results_if_simplified(
+            new_instruction,
+            block,
+            ctrl_typevars,
+            call_stack,
+            Some(id),
+        ) {
+            InsertInstructionResult::SimplifiedTo(new_result) => vec![new_result],
+            InsertInstructionResult::SimplifiedToMultiple(new_results) => new_results,
+            InsertInstructionResult::Results(_, new_results) => new_results.to_vec(),
+            InsertInstructionResult::InstructionRemoved => vec![],
+        };
+        // Optimizations while inserting the instruction should not change the number of results.
+        for (old_result, new_result) in old_results.iter().zip(new_results) {
+            function.dfg.set_value_from_id(*old_result, new_result);
+        }
+    }
+}
+
+fn simplify_binary(binary: Binary, dfg: &mut DataFlowGraph) -> Binary {
+    let Binary { lhs, rhs, operator } = binary;
+
+    if operator == BinaryOp::Div {
+        if let Some((rhs_value, NumericType::NativeField)) = dfg.get_numeric_constant_with_type(rhs)
+        {
+            if !rhs_value.is_zero() {
+                let rhs = dfg.make_constant(rhs_value.inverse(), NumericType::NativeField);
+                Binary { lhs, rhs, operator: BinaryOp::Mul { unchecked: false } }
+            } else {
+                binary
+            }
+        } else {
+            binary
+        }
+    } else {
+        binary
+    }
+}
+
+/// This method inspects the precursor instruction for binary instructions with a constant argument,
+/// where possible it will then combine the constants within the two instructions in order to flatten both operations.
+///
+/// # Example
+///
+/// Consider a program consisting of the instruction
+///
+/// ```md
+/// v1 = add v0, u32 1
+/// ```
+///
+/// If we insert the instruction defined as
+///
+/// ```md
+/// v2 = lt v1, u32 9
+/// ```
+///
+/// this can be automatically simplified to instead be
+///
+/// ```md
+/// v2 = lt v0, u32 8
+/// ```
+fn simplify_using_previous_instruction(binary: &Binary, dfg: &mut DataFlowGraph) -> SimplifyResult {
+    // We make some assumptions about the shape of binary instructions for simplicity, namely that any constant arguments are in the `rhs` term.
+    // This allows us to define the following structure for the pair of binary instructions.
+    let ((inner_lhs, inner_rhs, inner_operator), outer_rhs, outer_operator): (
+        (ValueId, FieldElement, BinaryOp),
+        FieldElement,
+        BinaryOp,
+    ) = match (&dfg[binary.lhs], &dfg[binary.rhs]) {
+        (
+            Value::Instruction { instruction, .. },
+            Value::NumericConstant { constant: outer_constant, .. },
+        ) => {
+            let Instruction::Binary(Binary { lhs, rhs, operator }) = dfg[*instruction].clone()
+            else {
+                return SimplifyResult::None;
+            };
+
+            let Value::NumericConstant { constant: inner_constant, .. } = dfg[rhs].clone() else {
+                return SimplifyResult::None;
+            };
+
+            ((lhs, inner_constant, operator), *outer_constant, binary.operator)
+        }
+
+        _ => return SimplifyResult::None,
+    };
+
+    let typ = dfg.type_of_value(inner_lhs).unwrap_numeric();
+
+    match outer_operator {
+        BinaryOp::Lt => {
+            if !matches!(inner_operator, BinaryOp::Add { .. }) {
+                return SimplifyResult::None;
+            }
+
+            if outer_rhs < inner_rhs {
+                // Skip if performing subtraction would result in an underflow.
+                return SimplifyResult::None;
+            }
+
+            let Some((new_const, new_typ)) = eval_constant_binary_op(
+                outer_rhs,
+                inner_rhs,
+                BinaryOp::Sub { unchecked: false },
+                typ,
+            ) else {
+                return SimplifyResult::None;
+            };
+            assert_eq!(typ, new_typ, "ICE: instruction type changed");
+
+            let new_const = dfg.make_constant(new_const, typ);
+            SimplifyResult::SimplifiedToInstruction(Instruction::binary(
+                BinaryOp::Lt,
+                inner_lhs,
+                new_const,
+            ))
+        }
+
+        // We can implement more of these optimizations however we only do this for a subset currently
+        _ => SimplifyResult::None,
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use crate::{assert_ssa_snapshot, ssa::ssa_gen::Ssa};
+
+    #[test]
+    fn remove_constant_divisions() {
+        // We want to replace any field divisions by constants with an equivalent multiplication so that we
+        // perform the field inversion at compile time.
+        let src = "
+        acir(inline) fn main f0 {
+          b0(v0: Field):
+            v1 = div v0, Field 2
+            return
+        }
+        ";
+        let ssa = Ssa::from_str(src).unwrap();
+
+        assert_ssa_snapshot!(ssa.arithmetic_optimization(), @r"
+        acir(inline) fn main f0 {
+          b0(v0: Field):
+            v2 = mul v0, Field 10944121435919637611123202872628637544274182200208017171849102093287904247809
+            return
+        }
+        ");
+    }
+
+    #[test]
+    fn cross_instruction_lt_optimization() {
+        // We want to test that the calculation of `v2` is rewritten to not depend on `v1` as we can combine the
+        // two constants into a new constant.
+        let src = "
+        acir(inline) fn main f0 {
+          b0(v0: u32):
+            v1 = add v0, u32 1
+            v2 = lt v1, u32 9
+            return
+        }
+        ";
+        let ssa = Ssa::from_str(src).unwrap();
+
+        // We preserve `v2` as this should be removed by the DIE optimization pass.
+        assert_ssa_snapshot!(ssa.arithmetic_optimization(), @r"
+        acir(inline) fn main f0 {
+          b0(v0: u32):
+            v2 = add v0, u32 1
+            v4 = lt v0, u32 8
+            return
+        }
+        ");
+    }
+}
diff --git a/compiler/noirc_evaluator/src/ssa/opt/mod.rs b/compiler/noirc_evaluator/src/ssa/opt/mod.rs
index d5f8386d990..0e60146eb82 100644
--- a/compiler/noirc_evaluator/src/ssa/opt/mod.rs
+++ b/compiler/noirc_evaluator/src/ssa/opt/mod.rs
@@ -4,6 +4,7 @@
 //! simpler form until the IR only has a single function remaining with 1 block within it.
 //! Generally, these passes are also expected to minimize the final amount of instructions.
 
+mod arithmetic;
 mod array_set;
 mod as_slice_length;
 mod assert_constant;
@@ -108,10 +109,10 @@ pub(crate) fn assert_normalized_ssa_equals(mut ssa: super::Ssa, expected: &str)
 /// ```
 #[macro_export]
 macro_rules! assert_ssa_snapshot {
-    ($ssa:expr, $($arg:tt)*) => {
+    ($ssa:expr, $($arg:tt)*) => {{
         #[allow(unused_mut)]
         let mut mut_ssa = $ssa;
         mut_ssa.normalize_ids();
         insta::assert_snapshot!(mut_ssa, $($arg)*)
-    };
+    }};
 }