Index: llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
===================================================================
--- llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
+++ llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
@@ -3471,6 +3471,10 @@
   return nullptr;
 }
 
+static bool hasCommonOperand(Value *A, Value *B, Value *C, Value *D) {
+  return A == C || A == D || B == C || B == D;
+}
+
 // Transform
 //   ~(x ^ y)
 // into:
@@ -3490,8 +3494,28 @@
     // Ok, good.
   } else if (InstCombiner::isFreeToInvert(Y, Y->hasOneUse())) {
     std::swap(X, Y);
-  } else
+  } else {
+    Value *A, *B, *C, *D;
+    // Canonicalize ~((A & B) ^ (A | ?)) -> (A & B) | ~(A | ?)
+    // 4 commuted variants
+    if (match(X, m_And(m_Value(A), m_Value(B))) &&
+        match(Y, m_Or(m_Value(C), m_Value(D))) &&
+        hasCommonOperand(A, B, C, D)) {
+      Value *NotY = Builder.CreateNot(Y);
+      return BinaryOperator::CreateOr(X, NotY);
+    };
+
+    // Canonicalize ~((A | ?) ^ (A & B)) -> (A & B) | ~(A | ?)
+    // 4 commuted variants
+    if (match(Y, m_And(m_Value(A), m_Value(B))) &&
+        match(X, m_Or(m_Value(C), m_Value(D))) &&
+        hasCommonOperand(A, B, C, D)) {
+      Value *NotX = Builder.CreateNot(X);
+      return BinaryOperator::CreateOr(Y, NotX);
+    };
+
     return nullptr;
+  }
 
   Value *NotX = Builder.CreateNot(X, X->getName() + ".not");
   return BinaryOperator::CreateXor(NotX, Y, I.getName() + ".demorgan");
Index: llvm/test/Transforms/InstCombine/xor2.ll
===================================================================
--- llvm/test/Transforms/InstCombine/xor2.ll
+++ llvm/test/Transforms/InstCombine/xor2.ll
@@ -519,3 +519,116 @@
   %res = mul i8 %and, %xor2 ; to increase the use count for the xor
   ret i8 %res
 }
+
+; Canonicalize ~(A & B) ^ (A | ?) -> (A & B) | ~(A | ?)
+
+define i3 @not_xor_to_or_not1(i3 %a, i3 %b, i3 %c) {
+; CHECK-LABEL: @not_xor_to_or_not1(
+; CHECK-NEXT:    [[OR:%.*]] = or i3 [[B:%.*]], [[C:%.*]]
+; CHECK-NEXT:    [[AND:%.*]] = and i3 [[A:%.*]], [[C]]
+; CHECK-NEXT:    [[TMP1:%.*]] = xor i3 [[OR]], -1
+; CHECK-NEXT:    [[NOT:%.*]] = or i3 [[AND]], [[TMP1]]
+; CHECK-NEXT:    ret i3 [[NOT]]
+;
+  %or = or i3 %b, %c
+  %and = and i3 %a, %c
+  %xor = xor i3 %and, %or
+  %not = xor i3 %xor, -1
+  ret i3 %not
+}
+
+define i3 @not_xor_to_or_not2(i3 %a, i3 %b, i3 %c) {
+; CHECK-LABEL: @not_xor_to_or_not2(
+; CHECK-NEXT:    [[OR:%.*]] = or i3 [[C:%.*]], [[B:%.*]]
+; CHECK-NEXT:    [[AND:%.*]] = and i3 [[A:%.*]], [[C]]
+; CHECK-NEXT:    [[TMP1:%.*]] = xor i3 [[OR]], -1
+; CHECK-NEXT:    [[NOT:%.*]] = or i3 [[AND]], [[TMP1]]
+; CHECK-NEXT:    ret i3 [[NOT]]
+;
+  %or = or i3 %c, %b
+  %and = and i3 %a, %c
+  %xor = xor i3 %and, %or
+  %not = xor i3 %xor, -1
+  ret i3 %not
+}
+
+define i3 @not_xor_to_or_not3(i3 %a, i3 %b, i3 %c) {
+; CHECK-LABEL: @not_xor_to_or_not3(
+; CHECK-NEXT:    [[OR:%.*]] = or i3 [[C:%.*]], [[B:%.*]]
+; CHECK-NEXT:    [[AND:%.*]] = and i3 [[C]], [[A:%.*]]
+; CHECK-NEXT:    [[TMP1:%.*]] = xor i3 [[OR]], -1
+; CHECK-NEXT:    [[NOT:%.*]] = or i3 [[AND]], [[TMP1]]
+; CHECK-NEXT:    ret i3 [[NOT]]
+;
+  %or = or i3 %c, %b
+  %and = and i3 %c, %a
+  %xor = xor i3 %and, %or
+  %not = xor i3 %xor, -1
+  ret i3 %not
+}
+
+define i3 @not_xor_to_or_not4(i3 %a, i3 %b, i3 %c) {
+; CHECK-LABEL: @not_xor_to_or_not4(
+; CHECK-NEXT:    [[OR:%.*]] = or i3 [[B:%.*]], [[C:%.*]]
+; CHECK-NEXT:    [[AND:%.*]] = and i3 [[C]], [[A:%.*]]
+; CHECK-NEXT:    [[TMP1:%.*]] = xor i3 [[OR]], -1
+; CHECK-NEXT:    [[NOT:%.*]] = or i3 [[AND]], [[TMP1]]
+; CHECK-NEXT:    ret i3 [[NOT]]
+;
+  %or = or i3 %b, %c
+  %and = and i3 %c, %a
+  %xor = xor i3 %and, %or
+  %not = xor i3 %xor, -1
+  ret i3 %not
+}
+
+define <3 x i5> @not_xor_to_or_not_vector(<3 x i5> %a, <3 x i5> %b, <3 x i5> %c) {
+; CHECK-LABEL: @not_xor_to_or_not_vector(
+; CHECK-NEXT:    [[OR:%.*]] = or <3 x i5> [[B:%.*]], [[C:%.*]]
+; CHECK-NEXT:    [[AND:%.*]] = and <3 x i5> [[A:%.*]], [[C]]
+; CHECK-NEXT:    [[TMP1:%.*]] = xor <3 x i5> [[OR]], <i5 -1, i5 -1, i5 -1>
+; CHECK-NEXT:    [[NOT:%.*]] = or <3 x i5> [[AND]], [[TMP1]]
+; CHECK-NEXT:    ret <3 x i5> [[NOT]]
+;
+  %or = or <3 x i5> %b, %c
+  %and = and <3 x i5> %a, %c
+  %xor = xor <3 x i5> %or, %and
+  %not = xor <3 x i5> %xor, <i5 -1, i5 -1, i5 -1>
+  ret <3 x i5> %not
+}
+
+define <3 x i5> @not_xor_to_or_not_vector_poison(<3 x i5> %a, <3 x i5> %b, <3 x i5> %c) {
+; CHECK-LABEL: @not_xor_to_or_not_vector_poison(
+; CHECK-NEXT:    [[OR:%.*]] = or <3 x i5> [[B:%.*]], [[C:%.*]]
+; CHECK-NEXT:    [[AND:%.*]] = and <3 x i5> [[A:%.*]], [[C]]
+; CHECK-NEXT:    [[TMP1:%.*]] = xor <3 x i5> [[OR]], <i5 -1, i5 -1, i5 -1>
+; CHECK-NEXT:    [[NOT:%.*]] = or <3 x i5> [[AND]], [[TMP1]]
+; CHECK-NEXT:    ret <3 x i5> [[NOT]]
+;
+  %or = or <3 x i5> %b, %c
+  %and = and <3 x i5> %a, %c
+  %xor = xor <3 x i5> %or, %and
+  %not = xor <3 x i5> %xor, <i5 poison, i5 -1, i5 -1>
+  ret <3 x i5> %not
+}
+
+; negative test: one-use
+
+define i3 @not_xor_to_or_not_2use(i3 %a, i3 %b, i3 %c) {
+; CHECK-LABEL: @not_xor_to_or_not_2use(
+; CHECK-NEXT:    [[OR:%.*]] = or i3 [[B:%.*]], [[C:%.*]]
+; CHECK-NEXT:    [[AND:%.*]] = and i3 [[A:%.*]], [[C]]
+; CHECK-NEXT:    [[XOR:%.*]] = xor i3 [[AND]], [[OR]]
+; CHECK-NEXT:    [[NOT:%.*]] = xor i3 [[XOR]], -1
+; CHECK-NEXT:    call void @use3(i3 [[XOR]])
+; CHECK-NEXT:    ret i3 [[NOT]]
+;
+  %or = or i3 %b, %c
+  %and = and i3 %a, %c
+  %xor = xor i3 %and, %or
+  %not = xor i3 %xor, -1
+  call void @use3(i3 %xor)
+  ret i3 %not
+}
+
+declare void @use3(i3)