diff --git a/llvm/lib/Analysis/InlineCost.cpp b/llvm/lib/Analysis/InlineCost.cpp
--- a/llvm/lib/Analysis/InlineCost.cpp
+++ b/llvm/lib/Analysis/InlineCost.cpp
@@ -387,6 +387,7 @@
   bool simplifyCallSite(Function *F, CallBase &Call);
   template <typename Callable>
   bool simplifyInstruction(Instruction &I, Callable Evaluate);
+  bool simplifyIntrinsicCallIsConstant(CallBase &CB);
   ConstantInt *stripAndComputeInBoundsConstantOffsets(Value *&V);
 
   /// Return true if the given argument to the function being considered for
@@ -1531,6 +1532,27 @@
   return true;
 }
 
+/// Try to simplify a call to llvm.is.constant.
+///
+/// Duplicate the argument checking from CallAnalyzer::simplifyCallSite since
+/// we expect calls of this specific intrinsic to be infrequent.
+///
+/// FIXME: Given that we know CB's parent (F) caller
+/// (CandidateCall->getParent()->getParent()), we might be able to determine
+/// whether inlining F into F's caller would change how the call to
+/// llvm.is.constant would evaluate.
+bool CallAnalyzer::simplifyIntrinsicCallIsConstant(CallBase &CB) {
+  Value *Arg = CB.getArgOperand(0);
+  auto *C = dyn_cast<Constant>(Arg);
+
+  if (!C)
+    C = dyn_cast_or_null<Constant>(SimplifiedValues.lookup(Arg));
+
+  Type *RT = CB.getFunctionType()->getReturnType();
+  SimplifiedValues[&CB] = ConstantInt::get(RT, C ? 1 : 0);
+  return true;
+}
+
 bool CallAnalyzer::visitBitCast(BitCastInst &I) {
   // Propagate constants through bitcasts.
   if (simplifyInstruction(I, [&](SmallVectorImpl<Constant *> &COps) {
@@ -2154,6 +2176,8 @@
       if (auto *SROAArg = getSROAArgForValueOrNull(II->getOperand(0)))
         SROAArgValues[II] = SROAArg;
       return true;
+    case Intrinsic::is_constant:
+      return simplifyIntrinsicCallIsConstant(Call);
     }
   }
 
diff --git a/llvm/test/Transforms/Inline/call-intrinsic-is-constant.ll b/llvm/test/Transforms/Inline/call-intrinsic-is-constant.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/Inline/call-intrinsic-is-constant.ll
@@ -0,0 +1,39 @@
+; RUN: opt %s -passes=inline -inline-threshold=20 -S | FileCheck %s
+
+declare i1 @llvm.is.constant.i64(i64)
+declare void @foo()
+
+define void @callee(i64 %val) {
+  %cond = call i1 @llvm.is.constant.i64(i64 %val)
+  br i1 %cond, label %cond.true, label %cond.false
+
+cond.true:
+; Rack up costs with a couple of function calls so that this function
+; gets inlined only when @llvm.is.constant.i64 is folded.  In reality,
+; the "then" clause of __builtin_constant_p tends to have statements
+; that fold very well, so the cost of the "then" clause is not a huge
+; concern.
+  call void @foo()
+  call void @foo()
+  ret void
+
+cond.false:
+  ret void
+}
+
+define void @caller(i64 %val) {
+; CHECK-LABEL: @caller(
+; CHECK-NEXT:    [[COND_I:%.*]] = call i1 @llvm.is.constant.i64(i64 [[VAL:%.*]])
+; CHECK-NEXT:    br i1 [[COND_I]], label %[[COND_TRUE_I:.*]], label %[[COND_FALSE_I:.*]]
+; CHECK:       [[COND_TRUE_I]]:
+; CHECK-NEXT:    call void @foo()
+; CHECK-NEXT:    call void @foo()
+; CHECK-NEXT:    br label %[[CALLEE_EXIT:.*]]
+; CHECK:       [[COND_FALSE_I]]:
+; CHECK-NEXT:    br label %[[CALLEE_EXIT]]
+; CHECK:       [[CALLEE_EXIT]]:
+; CHECK-NEXT:    ret void
+;
+  call void @callee(i64 %val)
+  ret void
+}