diff --git a/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp b/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
index 55afe1258159a..72f35f4e8e982 100644
--- a/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
@@ -5808,6 +5808,129 @@ static Instruction *foldICmpPow2Test(ICmpInst &I,
   return nullptr;
 }
 
+/// Find all possible pairs (BinOp, RHS) that BinOp V, RHS can be simplified.
+using OffsetOp = std::pair<Instruction::BinaryOps, Value *>;
+static void collectOffsetOp(Value *V, SmallVectorImpl<OffsetOp> &Offsets,
+                            bool AllowRecursion) {
+  Instruction *Inst = dyn_cast<Instruction>(V);
+  if (!Inst || !Inst->hasOneUse())
+    return;
+
+  switch (Inst->getOpcode()) {
+  case Instruction::Add:
+    if (isGuaranteedNotToBeUndefOrPoison(Inst->getOperand(1)))
+      Offsets.emplace_back(Instruction::Sub, Inst->getOperand(1));
+    if (isGuaranteedNotToBeUndefOrPoison(Inst->getOperand(0)))
+      Offsets.emplace_back(Instruction::Sub, Inst->getOperand(0));
+    break;
+  case Instruction::Sub:
+    if (isGuaranteedNotToBeUndefOrPoison(Inst->getOperand(1)))
+      Offsets.emplace_back(Instruction::Add, Inst->getOperand(1));
+    break;
+  case Instruction::Xor:
+    if (isGuaranteedNotToBeUndefOrPoison(Inst->getOperand(1)))
+      Offsets.emplace_back(Instruction::Xor, Inst->getOperand(1));
+    if (isGuaranteedNotToBeUndefOrPoison(Inst->getOperand(0)))
+      Offsets.emplace_back(Instruction::Xor, Inst->getOperand(0));
+    break;
+  case Instruction::Select:
+    if (AllowRecursion) {
+      collectOffsetOp(Inst->getOperand(1), Offsets, /*AllowRecursion=*/false);
+      collectOffsetOp(Inst->getOperand(2), Offsets, /*AllowRecursion=*/false);
+    }
+    break;
+  default:
+    break;
+  }
+}
+
+enum class OffsetKind { Invalid, Value, Select };
+
+struct OffsetResult {
+  OffsetKind Kind;
+  Value *V0, *V1, *V2;
+
+  static OffsetResult invalid() {
+    return {OffsetKind::Invalid, nullptr, nullptr, nullptr};
+  }
+  static OffsetResult value(Value *V) {
+    return {OffsetKind::Value, V, nullptr, nullptr};
+  }
+  static OffsetResult select(Value *Cond, Value *TrueV, Value *FalseV) {
+    return {OffsetKind::Select, Cond, TrueV, FalseV};
+  }
+  bool isValid() const { return Kind != OffsetKind::Invalid; }
+  Value *materialize(InstCombiner::BuilderTy &Builder) const {
+    switch (Kind) {
+    case OffsetKind::Invalid:
+      llvm_unreachable("Invalid offset result");
+    case OffsetKind::Value:
+      return V0;
+    case OffsetKind::Select:
+      return Builder.CreateSelect(V0, V1, V2);
+    }
+  }
+};
+
+/// Offset both sides of an equality icmp to see if we can save some
+/// instructions: icmp eq/ne X, Y -> icmp eq/ne X op Z, Y op Z.
+/// Note: This operation should not introduce poison.
+static Instruction *foldICmpEqualityWithOffset(ICmpInst &I,
+                                               InstCombiner::BuilderTy &Builder,
+                                               const SimplifyQuery &SQ) {
+  assert(I.isEquality() && "Expected an equality icmp");
+  Value *Op0 = I.getOperand(0), *Op1 = I.getOperand(1);
+  if (!Op0->getType()->isIntOrIntVectorTy())
+    return nullptr;
+
+  SmallVector<OffsetOp, 4> OffsetOps;
+  collectOffsetOp(Op0, OffsetOps, /*AllowRecursion=*/true);
+  collectOffsetOp(Op1, OffsetOps, /*AllowRecursion=*/true);
+
+  auto ApplyOffsetImpl = [&](Value *V, unsigned BinOpc, Value *RHS) -> Value * {
+    Value *Simplified = simplifyBinOp(BinOpc, V, RHS, SQ);
+    // Avoid infinite loops by checking if RHS is an identity for the BinOp.
+    if (!Simplified || Simplified == V)
+      return nullptr;
+    return Simplified;
+  };
+
+  auto ApplyOffset = [&](Value *V, unsigned BinOpc,
+                         Value *RHS) -> OffsetResult {
+    if (auto *Sel = dyn_cast<SelectInst>(V)) {
+      if (!Sel->hasOneUse())
+        return OffsetResult::invalid();
+      Value *TrueVal = ApplyOffsetImpl(Sel->getTrueValue(), BinOpc, RHS);
+      if (!TrueVal)
+        return OffsetResult::invalid();
+      Value *FalseVal = ApplyOffsetImpl(Sel->getFalseValue(), BinOpc, RHS);
+      if (!FalseVal)
+        return OffsetResult::invalid();
+      return OffsetResult::select(Sel->getCondition(), TrueVal, FalseVal);
+    }
+    if (Value *Simplified = ApplyOffsetImpl(V, BinOpc, RHS))
+      return OffsetResult::value(Simplified);
+    return OffsetResult::invalid();
+  };
+
+  for (auto [BinOp, RHS] : OffsetOps) {
+    auto BinOpc = static_cast<unsigned>(BinOp);
+
+    auto Op0Result = ApplyOffset(Op0, BinOpc, RHS);
+    if (!Op0Result.isValid())
+      continue;
+    auto Op1Result = ApplyOffset(Op1, BinOpc, RHS);
+    if (!Op1Result.isValid())
+      continue;
+
+    Value *NewLHS = Op0Result.materialize(Builder);
+    Value *NewRHS = Op1Result.materialize(Builder);
+    return new ICmpInst(I.getPredicate(), NewLHS, NewRHS);
+  }
+
+  return nullptr;
+}
+
 Instruction *InstCombinerImpl::foldICmpEquality(ICmpInst &I) {
   if (!I.isEquality())
     return nullptr;
@@ -6054,6 +6177,10 @@ Instruction *InstCombinerImpl::foldICmpEquality(ICmpInst &I) {
                                   : ConstantInt::getNullValue(A->getType()));
   }
 
+  if (auto *Res = foldICmpEqualityWithOffset(
+          I, Builder, getSimplifyQuery().getWithInstruction(&I)))
+    return Res;
+
   return nullptr;
 }
 
diff --git a/llvm/test/Transforms/InstCombine/icmp-add.ll b/llvm/test/Transforms/InstCombine/icmp-add.ll
index a8cdf80948a84..1a41c1f3e1045 100644
--- a/llvm/test/Transforms/InstCombine/icmp-add.ll
+++ b/llvm/test/Transforms/InstCombine/icmp-add.ll
@@ -2380,8 +2380,7 @@ define <2 x i1> @icmp_eq_add_non_splat(<2 x i32> %a) {
 
 define <2 x i1> @icmp_eq_add_undef2(<2 x i32> %a) {
 ; CHECK-LABEL: @icmp_eq_add_undef2(
-; CHECK-NEXT:    [[ADD:%.*]] = add <2 x i32> [[A:%.*]], splat (i32 5)
-; CHECK-NEXT:    [[CMP:%.*]] = icmp eq <2 x i32> [[ADD]], <i32 10, i32 undef>
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq <2 x i32> [[A:%.*]], <i32 5, i32 undef>
 ; CHECK-NEXT:    ret <2 x i1> [[CMP]]
 ;
   %add = add <2 x i32> %a, <i32 5, i32 5>
@@ -2391,8 +2390,7 @@ define <2 x i1> @icmp_eq_add_undef2(<2 x i32> %a) {
 
 define <2 x i1> @icmp_eq_add_non_splat2(<2 x i32> %a) {
 ; CHECK-LABEL: @icmp_eq_add_non_splat2(
-; CHECK-NEXT:    [[ADD:%.*]] = add <2 x i32> [[A:%.*]], splat (i32 5)
-; CHECK-NEXT:    [[CMP:%.*]] = icmp eq <2 x i32> [[ADD]], <i32 10, i32 11>
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq <2 x i32> [[A:%.*]], <i32 5, i32 6>
 ; CHECK-NEXT:    ret <2 x i1> [[CMP]]
 ;
   %add = add <2 x i32> %a, <i32 5, i32 5>
diff --git a/llvm/test/Transforms/InstCombine/icmp-equality-xor.ll b/llvm/test/Transforms/InstCombine/icmp-equality-xor.ll
index b8e8ed0eaf1da..b0b633fba06be 100644
--- a/llvm/test/Transforms/InstCombine/icmp-equality-xor.ll
+++ b/llvm/test/Transforms/InstCombine/icmp-equality-xor.ll
@@ -136,8 +136,7 @@ define i1 @foo2(i32 %x, i32 %y) {
 define <2 x i1> @foo3(<2 x i8> %x) {
 ; CHECK-LABEL: @foo3(
 ; CHECK-NEXT:  entry:
-; CHECK-NEXT:    [[XOR:%.*]] = xor <2 x i8> [[X:%.*]], <i8 -2, i8 -1>
-; CHECK-NEXT:    [[CMP:%.*]] = icmp ne <2 x i8> [[XOR]], <i8 9, i8 79>
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ne <2 x i8> [[X:%.*]], <i8 -9, i8 -80>
 ; CHECK-NEXT:    ret <2 x i1> [[CMP]]
 ;
 entry:
diff --git a/llvm/test/Transforms/InstCombine/icmp-select.ll b/llvm/test/Transforms/InstCombine/icmp-select.ll
index 0bdbc88ba67c6..ef6c149fd6558 100644
--- a/llvm/test/Transforms/InstCombine/icmp-select.ll
+++ b/llvm/test/Transforms/InstCombine/icmp-select.ll
@@ -628,3 +628,206 @@ define i1 @icmp_slt_select(i1 %cond, i32 %a, i32 %b) {
   %res = icmp slt i32 %lhs, %rhs
   ret i1 %res
 }
+
+define i1 @discr_eq(i8 %a, i8 %b) {
+; CHECK-LABEL: @discr_eq(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP1:%.*]] = icmp ugt i8 [[A:%.*]], 1
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp ugt i8 [[B:%.*]], 1
+; CHECK-NEXT:    [[TMP0:%.*]] = select i1 [[CMP1]], i8 [[A]], i8 3
+; CHECK-NEXT:    [[TMP1:%.*]] = select i1 [[CMP2]], i8 [[B]], i8 3
+; CHECK-NEXT:    [[RES:%.*]] = icmp eq i8 [[TMP0]], [[TMP1]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+entry:
+  %add1 = add i8 %a, -2
+  %cmp1 = icmp ugt i8 %a, 1
+  %sel1 = select i1 %cmp1, i8 %add1, i8 1
+  %add2 = add i8 %b, -2
+  %cmp2 = icmp ugt i8 %b, 1
+  %sel2 = select i1 %cmp2, i8 %add2, i8 1
+  %res = icmp eq i8 %sel1, %sel2
+  ret i1 %res
+}
+
+define i1 @discr_ne(i8 %a, i8 %b) {
+; CHECK-LABEL: @discr_ne(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP1:%.*]] = icmp ugt i8 [[A:%.*]], 1
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp ugt i8 [[B:%.*]], 1
+; CHECK-NEXT:    [[TMP0:%.*]] = select i1 [[CMP1]], i8 [[A]], i8 3
+; CHECK-NEXT:    [[TMP1:%.*]] = select i1 [[CMP2]], i8 [[B]], i8 3
+; CHECK-NEXT:    [[RES:%.*]] = icmp ne i8 [[TMP0]], [[TMP1]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+entry:
+  %add1 = add i8 %a, -2
+  %cmp1 = icmp ugt i8 %a, 1
+  %sel1 = select i1 %cmp1, i8 %add1, i8 1
+  %add2 = add i8 %b, -2
+  %cmp2 = icmp ugt i8 %b, 1
+  %sel2 = select i1 %cmp2, i8 %add2, i8 1
+  %res = icmp ne i8 %sel1, %sel2
+  ret i1 %res
+}
+
+define i1 @discr_xor_eq(i8 %a, i8 %b) {
+; CHECK-LABEL: @discr_xor_eq(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP1:%.*]] = icmp ugt i8 [[A:%.*]], 1
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp ugt i8 [[B:%.*]], 1
+; CHECK-NEXT:    [[TMP0:%.*]] = select i1 [[CMP1]], i8 [[A]], i8 -4
+; CHECK-NEXT:    [[TMP1:%.*]] = select i1 [[CMP2]], i8 [[B]], i8 -4
+; CHECK-NEXT:    [[RES:%.*]] = icmp eq i8 [[TMP0]], [[TMP1]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+entry:
+  %xor1 = xor i8 %a, -3
+  %cmp1 = icmp ugt i8 %a, 1
+  %sel1 = select i1 %cmp1, i8 %xor1, i8 1
+  %xor2 = xor i8 %b, -3
+  %cmp2 = icmp ugt i8 %b, 1
+  %sel2 = select i1 %cmp2, i8 %xor2, i8 1
+  %res = icmp eq i8 %sel1, %sel2
+  ret i1 %res
+}
+
+define i1 @discr_eq_simple(i8 %a, i8 %b) {
+; CHECK-LABEL: @discr_eq_simple(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[CMP1:%.*]] = icmp ugt i8 [[A:%.*]], 1
+; CHECK-NEXT:    [[TMP0:%.*]] = select i1 [[CMP1]], i8 [[A]], i8 3
+; CHECK-NEXT:    [[RES:%.*]] = icmp eq i8 [[TMP0]], [[B:%.*]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+entry:
+  %add1 = add i8 %a, -2
+  %cmp1 = icmp ugt i8 %a, 1
+  %sel1 = select i1 %cmp1, i8 %add1, i8 1
+  %add2 = add i8 %b, -2
+  %res = icmp eq i8 %sel1, %add2
+  ret i1 %res
+}
+
+define i1 @discr_eq_add_commuted(i8 noundef %a, i8 %b, i8 %c, i1 %cond1, i1 %cond2) {
+; CHECK-LABEL: @discr_eq_add_commuted(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[TMP0:%.*]] = select i1 [[COND1:%.*]], i8 [[B:%.*]], i8 0
+; CHECK-NEXT:    [[TMP1:%.*]] = select i1 [[COND2:%.*]], i8 [[C:%.*]], i8 [[B]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp eq i8 [[TMP0]], [[TMP1]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+entry:
+  %add1 = add i8 %a, %b
+  %sel1 = select i1 %cond1, i8 %add1, i8 %a
+  %add2 = add i8 %c, %a
+  %sel2 = select i1 %cond2, i8 %add2, i8 %add1
+  %res = icmp eq i8 %sel1, %sel2
+  ret i1 %res
+}
+
+define i1 @discr_eq_sub(i8 noundef %a, i8 %b, i8 %c, i1 %cond1, i1 %cond2) {
+; CHECK-LABEL: @discr_eq_sub(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[TMP0:%.*]] = select i1 [[COND1:%.*]], i8 [[B:%.*]], i8 0
+; CHECK-NEXT:    [[TMP1:%.*]] = select i1 [[COND2:%.*]], i8 [[C:%.*]], i8 0
+; CHECK-NEXT:    [[RES:%.*]] = icmp eq i8 [[TMP0]], [[TMP1]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+entry:
+  %neg = sub i8 0, %a
+  %sub1 = sub i8 %b, %a
+  %sel1 = select i1 %cond1, i8 %sub1, i8 %neg
+  %sub2 = sub i8 %c, %a
+  %sel2 = select i1 %cond2, i8 %sub2, i8 %neg
+  %res = icmp eq i8 %sel1, %sel2
+  ret i1 %res
+}
+
+; Negative tests
+
+define i1 @discr_eq_multi_use(i8 %a, i8 %b) {
+; CHECK-LABEL: @discr_eq_multi_use(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[ADD1:%.*]] = add i8 [[A:%.*]], -2
+; CHECK-NEXT:    [[CMP1:%.*]] = icmp ugt i8 [[A]], 1
+; CHECK-NEXT:    [[SEL1:%.*]] = select i1 [[CMP1]], i8 [[ADD1]], i8 1
+; CHECK-NEXT:    call void @use(i8 [[SEL1]])
+; CHECK-NEXT:    [[ADD2:%.*]] = add i8 [[B:%.*]], -2
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp ugt i8 [[B]], 1
+; CHECK-NEXT:    [[SEL2:%.*]] = select i1 [[CMP2]], i8 [[ADD2]], i8 1
+; CHECK-NEXT:    [[RES:%.*]] = icmp eq i8 [[SEL1]], [[SEL2]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+entry:
+  %add1 = add i8 %a, -2
+  %cmp1 = icmp ugt i8 %a, 1
+  %sel1 = select i1 %cmp1, i8 %add1, i8 1
+  call void @use(i8 %sel1)
+  %add2 = add i8 %b, -2
+  %cmp2 = icmp ugt i8 %b, 1
+  %sel2 = select i1 %cmp2, i8 %add2, i8 1
+  %res = icmp eq i8 %sel1, %sel2
+  ret i1 %res
+}
+
+define i1 @discr_eq_failed_to_simplify(i8 %a, i8 %b) {
+; CHECK-LABEL: @discr_eq_failed_to_simplify(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[ADD1:%.*]] = add i8 [[A:%.*]], -3
+; CHECK-NEXT:    [[CMP1:%.*]] = icmp ugt i8 [[A]], 1
+; CHECK-NEXT:    [[SEL1:%.*]] = select i1 [[CMP1]], i8 [[ADD1]], i8 1
+; CHECK-NEXT:    [[ADD2:%.*]] = add i8 [[B:%.*]], -2
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp ugt i8 [[B]], 1
+; CHECK-NEXT:    [[SEL2:%.*]] = select i1 [[CMP2]], i8 [[ADD2]], i8 1
+; CHECK-NEXT:    [[RES:%.*]] = icmp eq i8 [[SEL1]], [[SEL2]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+entry:
+  %add1 = add i8 %a, -3
+  %cmp1 = icmp ugt i8 %a, 1
+  %sel1 = select i1 %cmp1, i8 %add1, i8 1
+  %add2 = add i8 %b, -2
+  %cmp2 = icmp ugt i8 %b, 1
+  %sel2 = select i1 %cmp2, i8 %add2, i8 1
+  %res = icmp eq i8 %sel1, %sel2
+  ret i1 %res
+}
+
+define <2 x i1> @discr_eq_simple_vec(<2 x i8> %a, <2 x i8> %b, i1 %cond) {
+; CHECK-LABEL: @discr_eq_simple_vec(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[ADD1:%.*]] = add <2 x i8> [[A:%.*]], <i8 poison, i8 -2>
+; CHECK-NEXT:    [[SEL1:%.*]] = select i1 [[COND:%.*]], <2 x i8> [[ADD1]], <2 x i8> splat (i8 1)
+; CHECK-NEXT:    [[ADD2:%.*]] = add <2 x i8> [[B:%.*]], <i8 -2, i8 poison>
+; CHECK-NEXT:    [[RES:%.*]] = icmp eq <2 x i8> [[SEL1]], [[ADD2]]
+; CHECK-NEXT:    ret <2 x i1> [[RES]]
+;
+entry:
+  %add1 = add <2 x i8> %a, <i8 poison, i8 -2>
+  %sel1 = select i1 %cond, <2 x i8> %add1, <2 x i8> splat(i8 1)
+  %add2 = add <2 x i8> %b, <i8 -2, i8 poison>
+  %res = icmp eq <2 x i8> %sel1, %add2
+  ret <2 x i1> %res
+}
+
+define i1 @discr_eq_sub_commuted(i8 noundef %a, i8 %b, i8 %c, i1 %cond1, i1 %cond2) {
+; CHECK-LABEL: @discr_eq_sub_commuted(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[NEG:%.*]] = sub i8 0, [[A:%.*]]
+; CHECK-NEXT:    [[SUB1:%.*]] = sub i8 [[A]], [[B:%.*]]
+; CHECK-NEXT:    [[SEL1:%.*]] = select i1 [[COND1:%.*]], i8 [[SUB1]], i8 [[NEG]]
+; CHECK-NEXT:    [[SUB2:%.*]] = sub i8 [[A]], [[C:%.*]]
+; CHECK-NEXT:    [[SEL2:%.*]] = select i1 [[COND2:%.*]], i8 [[SUB2]], i8 [[NEG]]
+; CHECK-NEXT:    [[RES:%.*]] = icmp eq i8 [[SEL1]], [[SEL2]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+entry:
+  %neg = sub i8 0, %a
+  %sub1 = sub i8 %a, %b
+  %sel1 = select i1 %cond1, i8 %sub1, i8 %neg
+  %sub2 = sub i8 %a, %c
+  %sel2 = select i1 %cond2, i8 %sub2, i8 %neg
+  %res = icmp eq i8 %sel1, %sel2
+  ret i1 %res
+}