Index: llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
===================================================================
--- llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
+++ llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
@@ -3219,6 +3219,11 @@
     // ~(X + C) --> -(C + 1) - X
     if (match(Op0, m_Add(m_Value(X), m_Constant(C))))
       return BinaryOperator::CreateSub(ConstantExpr::getNeg(AddOne(C)), X);
+
+    // ~(~X + Y) --> X - Y
+    if (match(NotVal, m_c_Add(m_Not(m_Value(X)), m_Value(Y))))
+      return BinaryOperator::CreateWithCopiedFlags(Instruction::Sub, X, Y,
+                                                   NotVal);
   }
 
   // Use DeMorgan and reassociation to eliminate a 'not' op.
Index: llvm/test/Transforms/InstCombine/not-add.ll
===================================================================
--- /dev/null
+++ llvm/test/Transforms/InstCombine/not-add.ll
@@ -0,0 +1,128 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt -instcombine -S < %s | FileCheck %s
+
+declare void @use(i8)
+declare i8 @get()
+
+define i8 @basic(i8 %x, i8 %y) {
+; CHECK-LABEL: @basic(
+; CHECK-NEXT:    [[NOTA:%.*]] = sub i8 [[X:%.*]], [[Y:%.*]]
+; CHECK-NEXT:    ret i8 [[NOTA]]
+;
+  %notx = xor i8 %x, -1
+  %a = add i8 %notx, %y
+  %nota = xor i8 %a, -1
+  ret i8 %nota
+}
+
+define i8 @basic_com_add(i8 %x, i8 %y) {
+; CHECK-LABEL: @basic_com_add(
+; CHECK-NEXT:    [[NOTA:%.*]] = sub i8 [[Y:%.*]], [[X:%.*]]
+; CHECK-NEXT:    ret i8 [[NOTA]]
+;
+  %noty = xor i8 %y, -1
+  %a = add i8 %x, %noty
+  %nota = xor i8 %a, -1
+  ret i8 %nota
+}
+
+define i8 @basic_use_xor(i8 %x, i8 %y) {
+; CHECK-LABEL: @basic_use_xor(
+; CHECK-NEXT:    [[NOTX:%.*]] = xor i8 [[X:%.*]], -1
+; CHECK-NEXT:    call void @use(i8 [[NOTX]])
+; CHECK-NEXT:    [[NOTA:%.*]] = sub i8 [[X]], [[Y:%.*]]
+; CHECK-NEXT:    ret i8 [[NOTA]]
+;
+  %notx = xor i8 %x, -1
+  call void @use(i8 %notx)
+  %a = add i8 %notx, %y
+  %nota = xor i8 %a, -1
+  ret i8 %nota
+}
+
+define i8 @basic_use_add(i8 %x, i8 %y) {
+; CHECK-LABEL: @basic_use_add(
+; CHECK-NEXT:    [[NOTX:%.*]] = xor i8 [[X:%.*]], -1
+; CHECK-NEXT:    [[A:%.*]] = add i8 [[NOTX]], [[Y:%.*]]
+; CHECK-NEXT:    call void @use(i8 [[A]])
+; CHECK-NEXT:    [[NOTA:%.*]] = sub i8 [[X]], [[Y]]
+; CHECK-NEXT:    ret i8 [[NOTA]]
+;
+  %notx = xor i8 %x, -1
+  %a = add i8 %notx, %y
+  call void @use(i8 %a)
+  %nota = xor i8 %a, -1
+  ret i8 %nota
+}
+
+define i8 @basic_use_both(i8 %x, i8 %y) {
+; CHECK-LABEL: @basic_use_both(
+; CHECK-NEXT:    [[NOTX:%.*]] = xor i8 [[X:%.*]], -1
+; CHECK-NEXT:    call void @use(i8 [[NOTX]])
+; CHECK-NEXT:    [[A:%.*]] = add i8 [[NOTX]], [[Y:%.*]]
+; CHECK-NEXT:    call void @use(i8 [[A]])
+; CHECK-NEXT:    [[NOTA:%.*]] = sub i8 [[X]], [[Y]]
+; CHECK-NEXT:    ret i8 [[NOTA]]
+;
+  %notx = xor i8 %x, -1
+  call void @use(i8 %notx)
+  %a = add i8 %notx, %y
+  call void @use(i8 %a)
+  %nota = xor i8 %a, -1
+  ret i8 %nota
+}
+
+define i8 @basic_preserve_nsw(i8 %x, i8 %y) {
+; CHECK-LABEL: @basic_preserve_nsw(
+; CHECK-NEXT:    [[NOTA:%.*]] = sub nsw i8 [[X:%.*]], [[Y:%.*]]
+; CHECK-NEXT:    ret i8 [[NOTA]]
+;
+  %notx = xor i8 %x, -1
+  %a = add nsw i8 %notx, %y
+  %nota = xor i8 %a, -1
+  ret i8 %nota
+}
+
+define i8 @basic_preserve_nuw(i8 %x, i8 %y) {
+; CHECK-LABEL: @basic_preserve_nuw(
+; CHECK-NEXT:    [[NOTA:%.*]] = sub nuw i8 [[X:%.*]], [[Y:%.*]]
+; CHECK-NEXT:    ret i8 [[NOTA]]
+;
+  %notx = xor i8 %x, -1
+  %a = add nuw i8 %notx, %y
+  %nota = xor i8 %a, -1
+  ret i8 %nota
+}
+
+define i8 @basic_preserve_nuw_nsw(i8 %x, i8 %y) {
+; CHECK-LABEL: @basic_preserve_nuw_nsw(
+; CHECK-NEXT:    [[NOTA:%.*]] = sub nuw nsw i8 [[X:%.*]], [[Y:%.*]]
+; CHECK-NEXT:    ret i8 [[NOTA]]
+;
+  %notx = xor i8 %x, -1
+  %a = add nuw nsw i8 %notx, %y
+  %nota = xor i8 %a, -1
+  ret i8 %nota
+}
+
+define <4 x i32> @vector_test(<4 x i32> %x, <4 x i32> %y) {
+; CHECK-LABEL: @vector_test(
+; CHECK-NEXT:    [[NOTA:%.*]] = sub <4 x i32> [[X:%.*]], [[Y:%.*]]
+; CHECK-NEXT:    ret <4 x i32> [[NOTA]]
+;
+  %notx = xor <4 x i32> %x, <i32 -1, i32 -1, i32 -1, i32 -1>
+  %a = add <4 x i32> %notx, %y
+  %nota = xor <4 x i32> %a, <i32 -1, i32 -1, i32 -1, i32 -1>
+  ret <4 x i32> %nota
+}
+
+define <4 x i32> @vector_test_undef(<4 x i32> %x, <4 x i32> %y) {
+; CHECK-LABEL: @vector_test_undef(
+; CHECK-NEXT:    [[NOTA:%.*]] = sub <4 x i32> [[X:%.*]], [[Y:%.*]]
+; CHECK-NEXT:    ret <4 x i32> [[NOTA]]
+;
+  %notx = xor <4 x i32> %x, <i32 -1, i32 undef, i32 undef, i32 -1>
+  %a = add <4 x i32> %notx, %y
+  %nota = xor <4 x i32> %a, <i32 -1, i32 -1, i32 undef, i32 undef>
+  ret <4 x i32> %nota
+}