diff --git a/tensorflow/core/grappler/optimizers/shape_optimizer.cc b/tensorflow/core/grappler/optimizers/shape_optimizer.cc
index 3a1cfb64b99..4bcb4dfc791 100644
--- a/tensorflow/core/grappler/optimizers/shape_optimizer.cc
+++ b/tensorflow/core/grappler/optimizers/shape_optimizer.cc
@@ -42,12 +42,16 @@ Status ShapeOptimizer::Optimize(Cluster* cluster, const GrapplerItem& item,
   bool has_size = false;
   bool has_shape = false;
   bool has_prod = false;
+  auto is_int = [](const NodeDef& node) -> bool {
+    return node.attr().at("T").type() == DT_INT32 ||
+           node.attr().at("T").type() == DT_INT64;
+  };
   for (const NodeDef& node : item.graph.node()) {
     if (IsShape(node)) {
       has_shape = true;
-    } else if (IsProd(node)) {
+    } else if (IsProd(node) && is_int(node)) {
       has_prod = true;
-    } else if (IsDiv(node)) {
+    } else if (IsDiv(node) && is_int(node)) {
       has_div = true;
     } else if (IsSize(node)) {
       has_size = true;
diff --git a/tensorflow/core/grappler/utils.h b/tensorflow/core/grappler/utils.h
index 71dbefeb5d4..7a1b65e1729 100644
--- a/tensorflow/core/grappler/utils.h
+++ b/tensorflow/core/grappler/utils.h
@@ -22,6 +22,8 @@ limitations under the License.
 #include <unordered_set>
 #include <utility>
 #include <vector>
+
+#include "absl/strings/string_view.h"
 #include "absl/types/span.h"
 #include "tensorflow/core/framework/graph.pb.h"
 #include "tensorflow/core/framework/node_def.pb.h"
@@ -120,54 +122,45 @@ bool IsSameInput(const string& name1, const string& name2);
 
 // Returns the trailing position number (or zero if no number is present) if
 // NodeName(input_name) is equal to node_name. Returns -1 for control inputs.
-// Returns -2 if NodeName(input_name) is not equal to node_name.
-// Note: This function is used very heavily, and this hand-optimized
-// version is 3-4x faster than the version using Scanner, which it replaced.
-// This is worth the reduction in readability.
-inline int NodePositionIfSameNode(const string& input_name,
-                                  const string& node_name) {
-  if (input_name.empty()) return -2;
-  const bool is_ctrl = input_name[0] == '^';
-  auto input_it = is_ctrl ? input_name.begin() + 1 : input_name.begin();
-  auto node_it = node_name.begin();
-  if (node_name.empty() ||
-      std::distance(input_it, input_name.end()) < node_name.size()) {
+// Returns -2 if input_name is empty or NodeName(input_name) is not equal to
+// node_name.
+inline int NodePositionIfSameNode(absl::string_view input_name,
+                                  absl::string_view node_name) {
+  bool is_control = absl::StartsWith(input_name, "^");
+  if (is_control) input_name.remove_prefix(1);
+  if (input_name.empty() || node_name.empty() ||
+      input_name.size() < node_name.size()) {
     return -2;
   }
-  while (node_it != node_name.end()) {
-    if (*input_it++ != *node_it++) {
-      return -2;
-    }
+  TensorId id = ParseTensorName(input_name);
+  if (id.first != node_name) return -2;
+  if (is_control) return -1;
+  return id.second;
+}
+
+// Returns the node name and position in a single call.
+inline StringPiece ParseNodeNameAsStringPiece(absl::string_view name,
+                                              int* position) {
+  const bool is_control = absl::StartsWith(name, "^");
+  TensorId id = ParseTensorName(name);
+  if (position) {
+    *position = is_control ? -1 : id.second;
   }
-  if (input_it == input_name.end()) {
-    return is_ctrl ? -1 : 0;
-  } else if (*input_it++ == ':') {
-    StringPiece remaining(&(*input_it),
-                          std::distance(input_it, input_name.end()));
-    int position;
-    if (!strings::safe_strto32(remaining, &position)) {
-      return -2;
-    }
-    return is_ctrl ? -1 : position;
-  } else {
-    return -2;
+  if (is_control && id.second >= 0) {
+    id.first.remove_prefix(1);
   }
+  return id.first;
+}
+
+// Returns the node name and position in a single call.
+inline string ParseNodeName(const string& name, int* position) {
+  return string(ParseNodeNameAsStringPiece(name, position));
 }
 
 // Return the node name corresponding to 'name' if name is valid, or the empty
 // string otherwise.
 inline StringPiece NodeNameAsStringPiece(const string& name) {
-  static const string empty;
-  if (name.empty()) return StringPiece(empty);
-  const auto begin_it = name[0] == '^' ? name.begin() + 1 : name.begin();
-  auto end_it = begin_it;
-  while (end_it != name.end() && *end_it != ':') {
-    ++end_it;
-  }
-  if (end_it != name.end() && *end_it != ':') {
-    return StringPiece(empty);
-  }
-  return StringPiece(&(*begin_it), std::distance(begin_it, end_it));
+  return ParseNodeNameAsStringPiece(name, nullptr);
 }
 
 // Return the node name corresponding to 'name' if name is valid, or the empty
@@ -176,43 +169,6 @@ inline string NodeName(const string& name) {
   return string(NodeNameAsStringPiece(name));
 }
 
-// Returns the node name and position in a single call.
-// DEPRECATED(ezhulenev): Use TensorId and ParseTensorName.
-inline StringPiece ParseNodeNameAsStringPiece(const string& name,
-                                              int* position) {
-  static const string empty;
-  if (name.empty()) {
-    *position = 0;
-    return StringPiece(empty);
-  }
-  const bool is_ctrl = name[0] == '^';
-  const auto begin_it = is_ctrl ? name.begin() + 1 : name.begin();
-  *position = is_ctrl ? -1 : 0;
-  auto end_it = begin_it;
-  while (end_it != name.end() && *end_it != ':') {
-    ++end_it;
-  }
-  const StringPiece node_name(&(*begin_it), std::distance(begin_it, end_it));
-  if (end_it != name.end()) {
-    if (*end_it != ':') {
-      return StringPiece(empty);
-    } else if (!is_ctrl) {
-      ++end_it;
-      StringPiece remaining(&(*end_it), std::distance(end_it, name.end()));
-      if (!strings::safe_strto32(remaining, position)) {
-        return StringPiece(empty);
-      }
-    }
-  }
-  return node_name;
-}
-
-// Returns the node name and position in a single call.
-// DEPRECATED(ezhulenev): Use SafeTensorId and ParseTensorName.
-inline string ParseNodeName(const string& name, int* position) {
-  return string(ParseNodeNameAsStringPiece(name, position));
-}
-
 inline int NodePosition(const string& name) {
   int position;
   ParseNodeNameAsStringPiece(name, &position);
diff --git a/tensorflow/core/grappler/utils_test.cc b/tensorflow/core/grappler/utils_test.cc
index a65704147ea..777630ff98c 100644
--- a/tensorflow/core/grappler/utils_test.cc
+++ b/tensorflow/core/grappler/utils_test.cc
@@ -454,6 +454,16 @@ BM_NodePositionIfSameNode("^foo/bar/baz", "foo/bar/baz", Match_Ctrl);
 BM_NodePositionIfSameNode("blah", "foo/bar/baz", NoMatch_0);
 BM_NodePositionIfSameNode("foo/bar/baz/gnu", "foo/bar/baz", NoMatch_end);
 
+static void BM_NodeNameAsStringPiece(int iters, int size) {
+  string input(size + 3, 'x');
+  input[size] = ':';
+  for (int i = 0; i < iters; ++i) {
+    StringPiece node_name = NodeNameAsStringPiece(input);
+    CHECK_GT(node_name.size(), 0);
+  }
+}
+BENCHMARK(BM_NodeNameAsStringPiece)->Range(1, 1024);
+
 #define BM_ParseNodeNameAsStringPiece(I, NAME)                               \
   static void BM_ParseNodeNameAsStringPiece_##NAME(int iters) {              \
     string input = I;                                                        \