diff --git a/mlir/include/mlir/IR/OperationSupport.h b/mlir/include/mlir/IR/OperationSupport.h
--- a/mlir/include/mlir/IR/OperationSupport.h
+++ b/mlir/include/mlir/IR/OperationSupport.h
@@ -1197,7 +1197,11 @@
     // When provided, the location attached to the operation are ignored.
     IgnoreLocations = 1,
 
-    LLVM_MARK_AS_BITMASK_ENUM(/* LargestValue = */ IgnoreLocations)
+    // When provided, operands on commutative operations are checked with their
+    // pointers.
+    HandleCommutativeOps = 2,
+
+    LLVM_MARK_AS_BITMASK_ENUM(/* LargestValue = */ HandleCommutativeOps)
   };
 
   /// Compute a hash for the given operation.
diff --git a/mlir/lib/IR/OperationSupport.cpp b/mlir/lib/IR/OperationSupport.cpp
--- a/mlir/lib/IR/OperationSupport.cpp
+++ b/mlir/lib/IR/OperationSupport.cpp
@@ -635,7 +635,8 @@
   //   - Operands
   ValueRange operands = op->getOperands();
   SmallVector<Value> operandStorage;
-  if (op->hasTrait<mlir::OpTrait::IsCommutative>()) {
+  if (op->hasTrait<mlir::OpTrait::IsCommutative>() &&
+      (flags & OperationEquivalence::HandleCommutativeOps)) {
     operandStorage.append(operands.begin(), operands.end());
     llvm::sort(operandStorage, [](Value a, Value b) -> bool {
       return a.getAsOpaquePointer() < b.getAsOpaquePointer();
@@ -722,7 +723,8 @@
 
   ValueRange lhsOperands = lhs->getOperands(), rhsOperands = rhs->getOperands();
   SmallVector<Value> lhsOperandStorage, rhsOperandStorage;
-  if (lhs->hasTrait<mlir::OpTrait::IsCommutative>()) {
+  if (lhs->hasTrait<mlir::OpTrait::IsCommutative>() &&
+      (flags & OperationEquivalence::HandleCommutativeOps)) {
     lhsOperandStorage.append(lhsOperands.begin(), lhsOperands.end());
     llvm::sort(lhsOperandStorage, [](Value a, Value b) -> bool {
       return a.getAsOpaquePointer() < b.getAsOpaquePointer();
diff --git a/mlir/lib/Transforms/CSE.cpp b/mlir/lib/Transforms/CSE.cpp
--- a/mlir/lib/Transforms/CSE.cpp
+++ b/mlir/lib/Transforms/CSE.cpp
@@ -32,7 +32,8 @@
         const_cast<Operation *>(opC),
         /*hashOperands=*/OperationEquivalence::directHashValue,
         /*hashResults=*/OperationEquivalence::ignoreHashValue,
-        OperationEquivalence::IgnoreLocations);
+        OperationEquivalence::IgnoreLocations |
+            OperationEquivalence::HandleCommutativeOps);
   }
   static bool isEqual(const Operation *lhsC, const Operation *rhsC) {
     auto *lhs = const_cast<Operation *>(lhsC);
@@ -46,7 +47,8 @@
         const_cast<Operation *>(lhsC), const_cast<Operation *>(rhsC),
         /*mapOperands=*/OperationEquivalence::exactValueMatch,
         /*mapResults=*/OperationEquivalence::ignoreValueEquivalence,
-        OperationEquivalence::IgnoreLocations);
+        OperationEquivalence::IgnoreLocations |
+            OperationEquivalence::HandleCommutativeOps);
   }
 };
 } // namespace