diff --git a/llvm/include/llvm/Analysis/IRSimilarityIdentifier.h b/llvm/include/llvm/Analysis/IRSimilarityIdentifier.h
--- a/llvm/include/llvm/Analysis/IRSimilarityIdentifier.h
+++ b/llvm/include/llvm/Analysis/IRSimilarityIdentifier.h
@@ -768,6 +768,24 @@
   static bool compareCommutativeOperandMapping(OperandMapping A,
                                                OperandMapping B);
 
+  /// Compare the GVN of the assignment value in corresponding instructions in
+  /// IRSimilarityCandidates \p A and \p B and check that there exists a mapping
+  /// between the values and replaces the mapping with a one-to-one value if
+  /// needed.
+  ///
+  /// \param InstValA - The assignment GVN from the first IRSimilarityCandidate.
+  /// \param InstValB - The assignment GVN from the second
+  /// IRSimilarityCandidate.
+  /// \param [in,out] ValueNumberMappingA - A mapping of value numbers from 
+  /// candidate \p A to candidate \B.
+  /// \param [in,out] ValueNumberMappingB - A mapping of value numbers from 
+  /// candidate \p B to candidate \A.
+  /// \returns true if the IRSimilarityCandidates assignments are compatible.
+  static bool compareAssignmentMapping(
+      const unsigned InstValA, const unsigned &InstValB,
+      DenseMap<unsigned, DenseSet<unsigned>> &ValueNumberMappingA,
+      DenseMap<unsigned, DenseSet<unsigned>> &ValueNumberMappingB);
+
   /// Compare the relative locations in \p A and \p B and check that the
   /// distances match if both locations are contained in the region, and that
   /// the branches both point outside the region if they do not.
diff --git a/llvm/lib/Analysis/IRSimilarityIdentifier.cpp b/llvm/lib/Analysis/IRSimilarityIdentifier.cpp
--- a/llvm/lib/Analysis/IRSimilarityIdentifier.cpp
+++ b/llvm/lib/Analysis/IRSimilarityIdentifier.cpp
@@ -718,6 +718,34 @@
   return true;
 }
 
+bool IRSimilarityCandidate::compareAssignmentMapping(
+    const unsigned InstValA, const unsigned &InstValB,
+    DenseMap<unsigned, DenseSet<unsigned>> &ValueNumberMappingA,
+    DenseMap<unsigned, DenseSet<unsigned>> &ValueNumberMappingB) {
+  DenseMap<unsigned, DenseSet<unsigned>>::iterator ValueMappingIt;
+  bool WasInserted;
+  std::tie(ValueMappingIt, WasInserted) = ValueNumberMappingA.insert(
+      std::make_pair(InstValA, DenseSet<unsigned>({InstValB})));
+  if (!WasInserted && !ValueMappingIt->second.contains(InstValB))
+    return false;
+  else if (ValueMappingIt->second.size() != 1) {
+    for (unsigned OtherVal : ValueMappingIt->second) {
+      if (OtherVal == InstValB)
+        continue;
+      if (ValueNumberMappingA.find(OtherVal) == ValueNumberMappingA.end())
+        continue;
+      if (!ValueNumberMappingA[OtherVal].contains(InstValA))
+        continue;
+      ValueNumberMappingA[OtherVal].erase(InstValA);
+    }
+    ValueNumberMappingA.erase(ValueMappingIt);
+    std::tie(ValueMappingIt, WasInserted) = ValueNumberMappingA.insert(
+      std::make_pair(InstValA, DenseSet<unsigned>({InstValB})));
+  }
+
+  return true;
+}
+
 bool IRSimilarityCandidate::checkRelativeLocations(RelativeLocMapping A,
                                                    RelativeLocMapping B) {
   // Get the basic blocks the label refers to.
@@ -775,8 +803,6 @@
   // in one candidate to values in the other candidate.  If we create a set with
   // one element, and that same element maps to the original element in the
   // candidate we have a good mapping.
-  DenseMap<unsigned, DenseSet<unsigned>>::iterator ValueMappingIt;
-
 
   // Iterate over the instructions contained in each candidate
   unsigned SectionLength = A.getStartIdx() + A.getLength();
@@ -799,16 +825,13 @@
     unsigned InstValA = A.ValueToNumber.find(IA)->second;
     unsigned InstValB = B.ValueToNumber.find(IB)->second;
 
-    bool WasInserted;
     // Ensure that the mappings for the instructions exists.
-    std::tie(ValueMappingIt, WasInserted) = ValueNumberMappingA.insert(
-        std::make_pair(InstValA, DenseSet<unsigned>({InstValB})));
-    if (!WasInserted && !ValueMappingIt->second.contains(InstValB))
+    if (!compareAssignmentMapping(InstValA, InstValB, ValueNumberMappingA,
+                                  ValueNumberMappingB))
       return false;
-
-    std::tie(ValueMappingIt, WasInserted) = ValueNumberMappingB.insert(
-        std::make_pair(InstValB, DenseSet<unsigned>({InstValA})));
-    if (!WasInserted && !ValueMappingIt->second.contains(InstValA))
+    
+    if (!compareAssignmentMapping(InstValB, InstValA, ValueNumberMappingB,
+                                  ValueNumberMappingA))
       return false;
 
     // We have different paths for commutative instructions and non-commutative
diff --git a/llvm/test/Transforms/IROutliner/outlining-larger-size-commutative.ll b/llvm/test/Transforms/IROutliner/outlining-larger-size-commutative.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/IROutliner/outlining-larger-size-commutative.ll
@@ -0,0 +1,89 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt -S -p iroutliner,verify -ir-outlining-no-cost < %s | FileCheck %s
+
+; This test checks that commutative instructions where the operands are
+; swapped are outlined as the same function.
+
+; It also checks that non-commutative instructions outlined as different
+; functions when the operands are swapped;
+
+; These are identical functions, except that in the flipped functions,
+; the operands in the adds are commuted.  However, since add instructions
+; are commutative, we should still outline from all four as the same
+; instruction.
+
+define void @function1(i32 %a, i32 %b) {
+; CHECK-LABEL: @function1(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br label [[BLOCK_1:%.*]]
+; CHECK:       block_0:
+; CHECK-NEXT:    [[TMP0:%.*]] = add i32 [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    [[TMP1:%.*]] = add i32 [[TMP4:%.*]], 1
+; CHECK-NEXT:    [[TMP2:%.*]] = add i32 [[TMP0]], [[TMP0]]
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp sgt i32 [[TMP0]], [[TMP0]]
+; CHECK-NEXT:    br i1 [[TMP3]], label [[BLOCK_1]], label [[BLOCK_2:%.*]]
+; CHECK:       block_1:
+; CHECK-NEXT:    [[TMP4]] = phi i32 [ [[TMP1]], [[BLOCK_0:%.*]] ], [ 0, [[ENTRY:%.*]] ]
+; CHECK-NEXT:    call void @outlined_ir_func_0(i32 [[B]])
+; CHECK-NEXT:    br label [[BLOCK_0]]
+; CHECK:       block_2:
+; CHECK-NEXT:    [[TMP5:%.*]] = add i32 [[TMP2]], [[TMP2]]
+; CHECK-NEXT:    ret void
+;
+entry:
+  br label %block_1
+
+block_0:
+  %0 = add i32 %a, %b
+  %1 = add i32 %4, 1
+  %2 = add i32 %0, %0
+  %3 = icmp sgt i32 %0, %0
+  br i1 %3, label %block_1, label %block_2
+
+block_1:
+  %4 = phi i32 [ %1, %block_0 ], [ 0, %entry ]
+  %5 = add i32 %b, %b
+  br label %block_0
+
+block_2:
+  %6 = add i32 %2, %2
+  ret void
+}
+
+define void @function2(i32 %a, i32 %b) {
+; CHECK-LABEL: @function2(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br label [[BLOCK_1:%.*]]
+; CHECK:       block_0:
+; CHECK-NEXT:    [[TMP0:%.*]] = sub i32 [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    [[TMP1:%.*]] = add i32 1, [[TMP4:%.*]]
+; CHECK-NEXT:    [[TMP2:%.*]] = add i32 [[TMP0]], [[TMP0]]
+; CHECK-NEXT:    [[TMP3:%.*]] = icmp sgt i32 [[TMP0]], [[TMP0]]
+; CHECK-NEXT:    br i1 [[TMP3]], label [[BLOCK_1]], label [[BLOCK_2:%.*]]
+; CHECK:       block_1:
+; CHECK-NEXT:    [[TMP4]] = phi i32 [ [[TMP1]], [[BLOCK_0:%.*]] ], [ 0, [[ENTRY:%.*]] ]
+; CHECK-NEXT:    call void @outlined_ir_func_0(i32 [[B]])
+; CHECK-NEXT:    br label [[BLOCK_0]]
+; CHECK:       block_2:
+; CHECK-NEXT:    [[TMP5:%.*]] = sub i32 [[TMP2]], [[TMP2]]
+; CHECK-NEXT:    ret void
+;
+entry:
+  br label %block_1
+
+block_0:
+  %0 = sub i32 %a, %b
+  %1 = add i32 1, %4
+  %2 = add i32 %0, %0
+  %3 = icmp sgt i32 %0, %0
+  br i1 %3, label %block_1, label %block_2
+
+block_1:
+  %4 = phi i32 [ %1, %block_0 ], [ 0, %entry ]
+  %5 = add i32 %b, %b
+  br label %block_0
+
+block_2:
+  %6 = sub i32 %2, %2
+  ret void
+}