diff --git a/tensorflow/core/grappler/optimizers/arithmetic_optimizer.cc b/tensorflow/core/grappler/optimizers/arithmetic_optimizer.cc
index 9a088702e19..4a9d2907642 100644
--- a/tensorflow/core/grappler/optimizers/arithmetic_optimizer.cc
+++ b/tensorflow/core/grappler/optimizers/arithmetic_optimizer.cc
@@ -1762,7 +1762,8 @@ class HoistCWiseUnaryChainsStage : public ArithmeticOptimizerStage {
     const std::set<NodeDef*> consumers = ctx().node_map->GetOutputs(node_name);
     for (NodeDef* consumer : consumers) {
       for (int i = 0; i < consumer->input_size(); ++i) {
-        if (consumer->input(i) == node_name) {
+        if (consumer->input(i) == node_name &&
+            consumer->name() != NodeName(new_input)) {
           consumer->set_input(i, new_input);
           ctx().node_map->UpdateInput(consumer->name(), node_name, new_input);
         }
@@ -2907,7 +2908,8 @@ class OptimizeMaxOrMinOfMonotonicStage : public ArithmeticOptimizerStage {
     const std::set<NodeDef*> consumers = ctx().node_map->GetOutputs(node_name);
     for (NodeDef* consumer : consumers) {
       for (int i = 0; i < consumer->input_size(); ++i) {
-        if (consumer->input(i) == node_name && consumer->name() != new_input) {
+        if (consumer->input(i) == node_name &&
+            consumer->name() != NodeName(new_input)) {
           consumer->set_input(i, new_input);
           ctx().node_map->UpdateInput(consumer->name(), node_name, new_input);
         }