diff --git a/llvm/lib/Analysis/InstructionSimplify.cpp b/llvm/lib/Analysis/InstructionSimplify.cpp
--- a/llvm/lib/Analysis/InstructionSimplify.cpp
+++ b/llvm/lib/Analysis/InstructionSimplify.cpp
@@ -4582,6 +4582,22 @@
       return FalseVal;
   }
 
+  if (Pred == ICmpInst::Predicate::ICMP_EQ) {
+    Value *X;
+    Value *Y;
+    // select(X | Y == 0, X or Y, X | Y) -> X | Y
+    if (match(CondVal, m_ICmp(Pred, m_Specific(FalseVal), m_Zero())) &&
+        match(FalseVal, m_Or(m_Value(X), m_Value(Y))) &&
+        (TrueVal == X || TrueVal == Y))
+      return FalseVal;
+    // select(X & Y == -1, X or Y, X & Y) -> X & Y
+    if (Pred == ICmpInst::Predicate::ICMP_EQ &&
+        match(CondVal, m_ICmp(Pred, m_Specific(FalseVal), m_AllOnes())) &&
+        match(FalseVal, m_And(m_Value(X), m_Value(Y))) &&
+        (TrueVal == X || TrueVal == Y))
+      return FalseVal;
+  }
+
   return nullptr;
 }
 
diff --git a/llvm/test/Transforms/InstCombine/select_or_and.ll b/llvm/test/Transforms/InstCombine/select_or_and.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/InstCombine/select_or_and.ll
@@ -0,0 +1,154 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt -S -passes=instcombine < %s | FileCheck %s
+
+; select(Y | X == 0, X, Y | X)
+define i32 @select_or_1(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_or_1(
+; CHECK-NEXT:    [[TMP3:%.*]] = or i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    ret i32 [[TMP3]]
+;
+  %3 = or i32 %1, %0
+  %4 = icmp eq i32 %3, 0
+  %5 = select i1 %4, i32 %0, i32 %3
+  ret i32 %5
+}
+
+; select(Y | X == 0, Y, Y | X)
+define i32 @select_or_2(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_or_2(
+; CHECK-NEXT:    [[TMP3:%.*]] = or i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    ret i32 [[TMP3]]
+;
+  %3 = or i32 %1, %0
+  %4 = icmp eq i32 %3, 0
+  %5 = select i1 %4, i32 %1, i32 %3
+  ret i32 %5
+}
+
+; select(Y | X != 0, Y | X, X)
+define i32 @select_or_3(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_or_3(
+; CHECK-NEXT:    [[TMP3:%.*]] = or i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    ret i32 [[TMP3]]
+;
+  %3 = or i32 %1, %0
+  %4 = icmp ne i32 %3, 0
+  %5 = select i1 %4, i32 %3, i32 %0
+  ret i32 %5
+}
+
+; select(Y | X != 0, Y | X, Y)
+define i32 @select_or_4(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_or_4(
+; CHECK-NEXT:    [[TMP3:%.*]] = or i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    ret i32 [[TMP3]]
+;
+  %3 = or i32 %1, %0
+  %4 = icmp ne i32 %3, 0
+  %5 = select i1 %4, i32 %3, i32 %1
+  ret i32 %5
+}
+
+; select(Y | X == 0, Y | X, Y)
+define i32 @select_or_not_1(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_or_not_1(
+; CHECK-NEXT:    [[TMP3:%.*]] = or i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    [[TMP4:%.*]] = icmp eq i32 [[TMP3]], 0
+; CHECK-NEXT:    [[TMP5:%.*]] = select i1 [[TMP4]], i32 0, i32 [[TMP1]]
+; CHECK-NEXT:    ret i32 [[TMP5]]
+;
+  %3 = or i32 %1, %0
+  %4 = icmp eq i32 %3, 0
+  %5 = select i1 %4, i32 %3, i32 %1
+  ret i32 %5
+}
+; select(Y | X != 0, Y, Y | X)
+define i32 @select_or_not_2(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_or_not_2(
+; CHECK-NEXT:    [[TMP3:%.*]] = or i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    [[DOTNOT:%.*]] = icmp eq i32 [[TMP3]], 0
+; CHECK-NEXT:    [[TMP4:%.*]] = select i1 [[DOTNOT]], i32 0, i32 [[TMP1]]
+; CHECK-NEXT:    ret i32 [[TMP4]]
+;
+  %3 = or i32 %1, %0
+  %4 = icmp ne i32 %3, 0
+  %5 = select i1 %4, i32 %1, i32 %3
+  ret i32 %5
+}
+
+; select(Y & X == -1, X, Y & X)
+define i32 @select_and_1(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_and_1(
+; CHECK-NEXT:    [[TMP3:%.*]] = and i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    ret i32 [[TMP3]]
+;
+  %3 = and i32 %1, %0
+  %4 = icmp eq i32 %3, -1
+  %5 = select i1 %4, i32 %0, i32 %3
+  ret i32 %5
+}
+
+; select(Y & X == -1, Y, Y & X)
+define i32 @select_and_2(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_and_2(
+; CHECK-NEXT:    [[TMP3:%.*]] = and i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    ret i32 [[TMP3]]
+;
+  %3 = and i32 %1, %0
+  %4 = icmp eq i32 %3, -1
+  %5 = select i1 %4, i32 %1, i32 %3
+  ret i32 %5
+}
+
+
+; select(Y & X != -1, Y & X, X)
+define i32 @select_and_3(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_and_3(
+; CHECK-NEXT:    [[TMP3:%.*]] = and i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    ret i32 [[TMP3]]
+;
+  %3 = and i32 %1, %0
+  %4 = icmp ne i32 %3, -1
+  %5 = select i1 %4, i32 %3, i32 %0
+  ret i32 %5
+}
+
+; select(Y & X != -1, Y & X, Y)
+define i32 @select_and_4(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_and_4(
+; CHECK-NEXT:    [[TMP3:%.*]] = and i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    ret i32 [[TMP3]]
+;
+  %3 = and i32 %1, %0
+  %4 = icmp ne i32 %3, -1
+  %5 = select i1 %4, i32 %3, i32 %1
+  ret i32 %5
+}
+
+; select(Y & X != -1, Y, Y & X)
+define i32 @select_and_not_1(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_and_not_1(
+; CHECK-NEXT:    [[TMP3:%.*]] = and i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    [[TMP4:%.*]] = icmp eq i32 [[TMP3]], -1
+; CHECK-NEXT:    [[TMP5:%.*]] = select i1 [[TMP4]], i32 -1, i32 [[TMP1]]
+; CHECK-NEXT:    ret i32 [[TMP5]]
+;
+  %3 = and i32 %1, %0
+  %4 = icmp eq i32 %3, -1
+  %5 = select i1 %4, i32 %3, i32 %1
+  ret i32 %5
+}
+
+; select(Y & X != -1, Y, Y & X)
+define i32 @select_and_not_2(i32 %0, i32 %1) {
+; CHECK-LABEL: @select_and_not_2(
+; CHECK-NEXT:    [[TMP3:%.*]] = and i32 [[TMP1:%.*]], [[TMP0:%.*]]
+; CHECK-NEXT:    [[DOTNOT:%.*]] = icmp eq i32 [[TMP3]], -1
+; CHECK-NEXT:    [[TMP4:%.*]] = select i1 [[DOTNOT]], i32 -1, i32 [[TMP1]]
+; CHECK-NEXT:    ret i32 [[TMP4]]
+;
+  %3 = and i32 %1, %0
+  %4 = icmp ne i32 %3, -1
+  %5 = select i1 %4, i32 %1, i32 %3
+  ret i32 %5
+}