Index: llvm/lib/Analysis/IRSimilarityIdentifier.cpp
===================================================================
--- llvm/lib/Analysis/IRSimilarityIdentifier.cpp
+++ llvm/lib/Analysis/IRSimilarityIdentifier.cpp
@@ -785,11 +785,39 @@
         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})));
+    }
 
     std::tie(ValueMappingIt, WasInserted) = ValueNumberMappingB.insert(
         std::make_pair(InstValB, DenseSet<unsigned>({InstValA})));
     if (!WasInserted && !ValueMappingIt->second.contains(InstValA))
       return false;
+    else if (ValueMappingIt->second.size() != 1) {
+      for (unsigned OtherVal : ValueMappingIt->second) {
+        if (OtherVal == InstValA)
+          continue;
+        if (ValueNumberMappingB.find(OtherVal) == ValueNumberMappingB.end())
+          continue;
+        if (!ValueNumberMappingB[OtherVal].contains(InstValB))
+          continue;
+        ValueNumberMappingB[OtherVal].erase(InstValB);
+      }
+      ValueNumberMappingB.erase(ValueMappingIt);
+      std::tie(ValueMappingIt, WasInserted) = ValueNumberMappingB.insert(
+        std::make_pair(InstValB, DenseSet<unsigned>({InstValA})));
+    }
 
     // We have different paths for commutative instructions and non-commutative
     // instructions since commutative instructions could allow multiple mappings
Index: llvm/test/Transforms/IROutliner/outlining-larger-size-commutative.ll
===================================================================
--- /dev/null
+++ 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
+}