diff --git a/barretenberg/cpp/src/barretenberg/proof_system/circuit_builder/ultra_circuit_builder.cpp b/barretenberg/cpp/src/barretenberg/proof_system/circuit_builder/ultra_circuit_builder.cpp
index e51cacc67d47..78c3f3ba3705 100644
--- a/barretenberg/cpp/src/barretenberg/proof_system/circuit_builder/ultra_circuit_builder.cpp
+++ b/barretenberg/cpp/src/barretenberg/proof_system/circuit_builder/ultra_circuit_builder.cpp
@@ -1665,8 +1665,8 @@ void UltraCircuitBuilder_<Arithmetization>::process_non_native_field_multiplicat
             c.b[j] = this->real_variable_index[c.b[j]];
         }
     }
-    std::sort(cached_partial_non_native_field_multiplications.begin(),
-              cached_partial_non_native_field_multiplications.end());
+    std::stable_sort(cached_partial_non_native_field_multiplications.begin(),
+                     cached_partial_non_native_field_multiplications.end());
 
     auto last = std::unique(cached_partial_non_native_field_multiplications.begin(),
                             cached_partial_non_native_field_multiplications.end());
diff --git a/barretenberg/cpp/src/barretenberg/proof_system/circuit_builder/ultra_circuit_builder.hpp b/barretenberg/cpp/src/barretenberg/proof_system/circuit_builder/ultra_circuit_builder.hpp
index 25c35737a128..41b43a0d683c 100644
--- a/barretenberg/cpp/src/barretenberg/proof_system/circuit_builder/ultra_circuit_builder.hpp
+++ b/barretenberg/cpp/src/barretenberg/proof_system/circuit_builder/ultra_circuit_builder.hpp
@@ -211,12 +211,13 @@ class UltraCircuitBuilder_ : public CircuitBuilderBase<typename Arithmetization:
             if (a < other.a) {
                 return true;
             }
-            if (a == other.a) {
-                if (b < other.b) {
-                    return true;
-                }
+            if (other.a < a) {
+                return false;
+            }
+            if (b < other.b) {
+                return true;
             }
-            return false;
+            return other.b < b;
         }
     };