chore: deterministically deduplicate cached_partial_non_native_field_multiplication across wasm32 and native compilations

barretenberg/cpp/src/barretenberg/proof_system/circuit_builder/ultra_circuit_builder.hpp

@@ -211,12 +211,31 @@ 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;
+            }
+            if (other.b < b) {
+                return false;
+            }
+
+            if (uint256_t(lo_0) < uint256_t(other.lo_0)) {
+                return true;
             }
-            return false;
+            if (uint256_t(other.lo_0) < uint256_t(lo_0)) {
+                return false;
+            }
+
+            if (uint256_t(hi_0) < uint256_t(other.hi_0)) {
+                return true;
+            }
+            if (uint256_t(other.hi_0) < uint256_t(hi_0)) {
+                return false;
+            }
+
+            return uint256_t(hi_1) < uint256_t(other.hi_1);
         }
     };