diff --git a/compiler/noirc_evaluator/src/ssa/acir_gen/acir_ir/acir_variable.rs b/compiler/noirc_evaluator/src/ssa/acir_gen/acir_ir/acir_variable.rs
index 05a22ab6aad..c9eed69e77c 100644
--- a/compiler/noirc_evaluator/src/ssa/acir_gen/acir_ir/acir_variable.rs
+++ b/compiler/noirc_evaluator/src/ssa/acir_gen/acir_ir/acir_variable.rs
@@ -368,6 +368,21 @@ impl AcirContext {
         rhs: AcirVar,
         typ: AcirType,
     ) -> Result<AcirVar, RuntimeError> {
+        let lhs_expr = self.var_to_expression(lhs)?;
+        let rhs_expr = self.var_to_expression(rhs)?;
+
+        if lhs_expr == rhs_expr {
+            // x ^ x == 0
+            let zero = self.add_constant(FieldElement::zero());
+            return Ok(zero);
+        } else if lhs_expr.is_zero() {
+            // 0 ^ x == x
+            return Ok(rhs);
+        } else if rhs_expr.is_zero() {
+            // x ^ 0 == x
+            return Ok(lhs);
+        }
+
         let inputs = vec![AcirValue::Var(lhs, typ.clone()), AcirValue::Var(rhs, typ)];
         let outputs = self.black_box_function(BlackBoxFunc::XOR, inputs, 1)?;
         Ok(outputs[0])
@@ -380,6 +395,18 @@ impl AcirContext {
         rhs: AcirVar,
         typ: AcirType,
     ) -> Result<AcirVar, RuntimeError> {
+        let lhs_expr = self.var_to_expression(lhs)?;
+        let rhs_expr = self.var_to_expression(rhs)?;
+
+        if lhs_expr == rhs_expr {
+            // x & x == x
+            return Ok(lhs);
+        } else if lhs_expr.is_zero() || rhs_expr.is_zero() {
+            // x & 0 == 0 and 0 & x == 0
+            let zero = self.add_constant(FieldElement::zero());
+            return Ok(zero);
+        }
+
         let bit_size = typ.bit_size();
         if bit_size == 1 {
             // Operands are booleans.
@@ -398,6 +425,16 @@ impl AcirContext {
         rhs: AcirVar,
         typ: AcirType,
     ) -> Result<AcirVar, RuntimeError> {
+        let lhs_expr = self.var_to_expression(lhs)?;
+        let rhs_expr = self.var_to_expression(rhs)?;
+        if lhs_expr.is_zero() {
+            // 0 | x == x
+            return Ok(rhs);
+        } else if rhs_expr.is_zero() {
+            // x | 0 == x
+            return Ok(lhs);
+        }
+
         let bit_size = typ.bit_size();
         if bit_size == 1 {
             // Operands are booleans