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
@@ -633,8 +633,18 @@
       op->getName(), op->getAttrDictionary(), op->getResultTypes());
 
   //   - Operands
-  for (Value operand : op->getOperands())
-    hash = llvm::hash_combine(hash, hashOperands(operand));
+  if (op->hasTrait<mlir::OpTrait::IsCommutative>()) {
+    llvm::SmallVector<void *> vec;
+    for (auto i = op->operand_begin(), e = op->operand_end(); i != e; ++i)
+      vec.push_back((*i).getAsOpaquePointer());
+    llvm::sort(vec.begin(), vec.end());
+    hash = llvm::hash_combine(hash,
+                              llvm::hash_combine_range(vec.begin(), vec.end()));
+  } else {
+    for (Value operand : op->getOperands())
+      hash = llvm::hash_combine(hash, hashOperands(operand));
+  }
+
   //   - Operands
   for (Value result : op->getResults())
     hash = llvm::hash_combine(hash, hashResults(result));
diff --git a/mlir/test/Transforms/cse.mlir b/mlir/test/Transforms/cse.mlir
--- a/mlir/test/Transforms/cse.mlir
+++ b/mlir/test/Transforms/cse.mlir
@@ -265,3 +265,16 @@
   }
   return
 } 
+
+
+/// This test is checking that identical commutative operation are gracefully
+/// handled but the CSE pass.
+// CHECK-LABEL: func @check_cummutative_cse
+func @check_cummutative_cse(%a : i32, %b : i32) -> i32 {
+  // CHECK: %[[ADD1:.*]] = arith.addi %{{.*}}, %{{.*}} : i32
+  %1 = arith.addi %a, %b : i32
+  %2 = arith.addi %b, %a : i32
+  // CHECK-NEXT:  arith.muli i32 %[[ADD1]], %[[ADD1]] : i32
+  %3 = arith.muli %1, %2 : i32
+  return %3 : i32
+}