diff --git a/llvm/lib/Analysis/InstructionSimplify.cpp b/llvm/lib/Analysis/InstructionSimplify.cpp
index 90baa054eed4c..311064eebf99d 100644
--- a/llvm/lib/Analysis/InstructionSimplify.cpp
+++ b/llvm/lib/Analysis/InstructionSimplify.cpp
@@ -2557,6 +2557,14 @@ static Value *simplifyXorInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
       return X;
   }
 
+  // (xor (or disjoint X, Y), Y) -> X
+  {
+    Value *X;
+    if (match(Op0, m_c_DisjointOr(m_Value(X), m_Specific(Op1))) ||
+        match(Op1, m_c_DisjointOr(m_Value(X), m_Specific(Op0))))
+      return X;
+  }
+
   return nullptr;
 }
 
diff --git a/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp b/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
index c6f317a668cfe..e87e31e162c29 100644
--- a/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
@@ -5866,6 +5866,24 @@ static void collectOffsetOp(Value *V, SmallVectorImpl<OffsetOp> &Offsets,
     Offsets.emplace_back(Instruction::Xor, Inst->getOperand(1));
     Offsets.emplace_back(Instruction::Xor, Inst->getOperand(0));
     break;
+  case Instruction::Or:
+    if (cast<PossiblyDisjointInst>(Inst)->isDisjoint())
+      Offsets.emplace_back(Instruction::Xor, Inst->getOperand(1));
+    Offsets.emplace_back(Instruction::Xor, Inst->getOperand(0));
+    break;
+  case Instruction::Shl:
+    if (auto *OBO = cast<OverflowingBinaryOperator>(Inst)) {
+      if (OBO->hasNoSignedWrap())
+        Offsets.emplace_back(Instruction::AShr, Inst->getOperand(1));
+      else if (OBO->hasNoUnsignedWrap())
+        Offsets.emplace_back(Instruction::LShr, Inst->getOperand(1));
+    }
+    break;
+  case Instruction::AShr:
+  case Instruction::LShr:
+    if (auto *PEO = cast<PossiblyExactOperator>(Inst); PEO && PEO->isExact())
+      Offsets.emplace_back(Instruction::Shl, Inst->getOperand(1));
+    break;
   case Instruction::Select:
     if (AllowRecursion) {
       collectOffsetOp(Inst->getOperand(1), Offsets, /*AllowRecursion=*/false);
diff --git a/llvm/test/Transforms/InstCombine/icmp-select.ll b/llvm/test/Transforms/InstCombine/icmp-select.ll
index a038731abbc48..2a4009d24fcf2 100644
--- a/llvm/test/Transforms/InstCombine/icmp-select.ll
+++ b/llvm/test/Transforms/InstCombine/icmp-select.ll
@@ -836,3 +836,63 @@ define i1 @discr_eq_constantexpr(ptr %p) {
   %cmp = icmp eq i64 %sub, -1
   ret i1 %cmp
 }
+
+define i1 @or_disjoint_eq(i8 %a, i1 %cond) {
+; CHECK-LABEL: @or_disjoint_eq(
+; CHECK-NEXT:    [[TMP1:%.*]] = select i1 [[COND:%.*]], i8 8, i8 4
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[A:%.*]], [[TMP1]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %or = or disjoint i8 %a, 3
+  %sel = select i1 %cond, i8 11, i8 7
+  %cmp = icmp eq i8 %or, %sel
+  ret i1 %cmp
+}
+
+define i1 @shl_nsw_eq(i8 %a, i1 %cond) {
+; CHECK-LABEL: @shl_nsw_eq(
+; CHECK-NEXT:    [[TMP1:%.*]] = select i1 [[COND:%.*]], i8 1, i8 2
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[A:%.*]], [[TMP1]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %a_shl = shl nsw i8 %a, 3
+  %sel = select i1 %cond, i8 8, i8 16
+  %cmp = icmp eq i8 %a_shl, %sel
+  ret i1 %cmp
+}
+
+define i1 @shl_nuw_eq(i8 %a, i1 %cond) {
+; CHECK-LABEL: @shl_nuw_eq(
+; CHECK-NEXT:    [[TMP1:%.*]] = select i1 [[COND:%.*]], i8 1, i8 4
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[A:%.*]], [[TMP1]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %a_shl = shl nuw i8 %a, 3
+  %sel = select i1 %cond, i8 8, i8 32
+  %cmp = icmp eq i8 %a_shl, %sel
+  ret i1 %cmp
+}
+
+define i1 @ashr_exact_eq(i8 %a, i1 %cond) {
+; CHECK-LABEL: @ashr_exact_eq(
+; CHECK-NEXT:    [[TMP1:%.*]] = select i1 [[COND:%.*]], i8 48, i8 16
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[A:%.*]], [[TMP1]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %a_shl = ashr exact i8 %a, 2
+  %sel = select i1 %cond, i8 12, i8 4
+  %cmp = icmp eq i8 %a_shl, %sel
+  ret i1 %cmp
+}
+
+define i1 @lshr_exact_eq(i8 %a, i1 %cond) {
+; CHECK-LABEL: @lshr_exact_eq(
+; CHECK-NEXT:    [[TMP1:%.*]] = select i1 [[COND:%.*]], i8 48, i8 16
+; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[A:%.*]], [[TMP1]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %a_shl = lshr exact i8 %a, 2
+  %sel = select i1 %cond, i8 12, i8 4
+  %cmp = icmp eq i8 %a_shl, %sel
+  ret i1 %cmp
+}
diff --git a/llvm/test/Transforms/InstSimplify/xor.ll b/llvm/test/Transforms/InstSimplify/xor.ll
index eaa016b6614e1..c7b0766bb65c4 100644
--- a/llvm/test/Transforms/InstSimplify/xor.ll
+++ b/llvm/test/Transforms/InstSimplify/xor.ll
@@ -301,3 +301,21 @@ define <2 x i4> @xor_or_and_not_poison_elt(<2 x i4> %a, <2 x i4> %b) {
   %r = xor <2 x i4> %or, %and
   ret <2 x i4> %r
 }
+
+define i8 @xor_or_disjoint(i8 %a, i8 %b) {
+; CHECK-LABEL: @xor_or_disjoint(
+; CHECK-NEXT:    ret i8 [[B:%.*]]
+;
+  %or = or disjoint i8 %a, %b
+  %xor = xor i8 %or, %a
+  ret i8 %xor
+}
+
+define i8 @xor_or_disjoint_c(i8 %a, i8 %b) {
+; CHECK-LABEL: @xor_or_disjoint_c(
+; CHECK-NEXT:    ret i8 [[B:%.*]]
+;
+  %or = or disjoint i8 %b, %a
+  %xor = xor i8 %a, %or
+  ret i8 %xor
+}