diff --git a/llvm/include/llvm/Transforms/IPO/FunctionSpecialization.h b/llvm/include/llvm/Transforms/IPO/FunctionSpecialization.h
--- a/llvm/include/llvm/Transforms/IPO/FunctionSpecialization.h
+++ b/llvm/include/llvm/Transforms/IPO/FunctionSpecialization.h
@@ -143,6 +143,8 @@
   Cost estimateBranchInst(BranchInst &I);
 
   Constant *visitInstruction(Instruction &I) { return nullptr; }
+  Constant *visitFreezeInst(FreezeInst &I);
+  Constant *visitCallBase(CallBase &I);
   Constant *visitLoadInst(LoadInst &I);
   Constant *visitGetElementPtrInst(GetElementPtrInst &I);
   Constant *visitSelectInst(SelectInst &I);
diff --git a/llvm/lib/Transforms/IPO/FunctionSpecialization.cpp b/llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
--- a/llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
+++ b/llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
@@ -222,6 +222,34 @@
   return estimateBasicBlocks(WorkList, KnownConstants, Solver, BFI, TTI);
 }
 
+Constant *InstCostVisitor::visitFreezeInst(FreezeInst &I) {
+  if (isGuaranteedNotToBeUndefOrPoison(LastVisited->second))
+    return LastVisited->second;
+  return nullptr;
+}
+
+Constant *InstCostVisitor::visitCallBase(CallBase &I) {
+  Function *F = I.getCalledFunction();
+  if (!F || !canConstantFoldCallTo(&I, F))
+    return nullptr;
+
+  SmallVector<Constant *, 8> Operands;
+  Operands.reserve(I.getNumOperands());
+
+  for (unsigned Idx = 0, E = I.getNumOperands() - 1; Idx != E; ++Idx) {
+    Value *V = I.getOperand(Idx);
+    auto *C = dyn_cast<Constant>(V);
+    if (!C)
+      C = findConstantFor(V, KnownConstants);
+    if (!C)
+      return nullptr;
+    Operands.push_back(C);
+  }
+
+  auto Ops = ArrayRef(Operands.begin(), Operands.end());
+  return ConstantFoldCall(&I, F, Ops);
+}
+
 Constant *InstCostVisitor::visitLoadInst(LoadInst &I) {
   if (isa<ConstantPointerNull>(LastVisited->second))
     return nullptr;
diff --git a/llvm/unittests/Transforms/IPO/FunctionSpecializationTest.cpp b/llvm/unittests/Transforms/IPO/FunctionSpecializationTest.cpp
--- a/llvm/unittests/Transforms/IPO/FunctionSpecializationTest.cpp
+++ b/llvm/unittests/Transforms/IPO/FunctionSpecializationTest.cpp
@@ -227,13 +227,21 @@
   const char *ModuleString = R"(
     @g = constant [2 x i32] zeroinitializer, align 4
 
-    define i32 @foo(i8 %a, i1 %cond, ptr %b) {
+    declare i32 @llvm.smax.i32(i32, i32)
+    declare i32 @bar(i32)
+
+    define i32 @foo(i8 %a, i1 %cond, ptr %b, i32 %c) {
       %cmp = icmp eq i8 %a, 10
       %ext = zext i1 %cmp to i32
       %sel = select i1 %cond, i32 %ext, i32 1
       %gep = getelementptr i32, ptr %b, i32 %sel
       %ld = load i32, ptr %gep
-      ret i32 %ld
+      %fr = freeze i32 %ld
+      %smax = call i32 @llvm.smax.i32(i32 %fr, i32 1)
+      %call = call i32 @bar(i32 %smax)
+      %fr2 = freeze i32 %c
+      %add = add i32 %call, %fr2
+      ret i32 %add
     }
   )";
 
@@ -245,6 +253,7 @@
   GlobalVariable *GV = M.getGlobalVariable("g");
   Constant *One = ConstantInt::get(IntegerType::getInt8Ty(M.getContext()), 1);
   Constant *True = ConstantInt::getTrue(M.getContext());
+  Constant *Undef = UndefValue::get(IntegerType::getInt32Ty(M.getContext()));
 
   auto BlockIter = F->front().begin();
   Instruction &Icmp = *BlockIter++;
@@ -252,6 +261,8 @@
   Instruction &Select = *BlockIter++;
   Instruction &Gep = *BlockIter++;
   Instruction &Load = *BlockIter++;
+  Instruction &Freeze = *BlockIter++;
+  Instruction &Smax = *BlockIter++;
 
   // icmp + zext
   Cost Ref = getInstCost(Icmp) + getInstCost(Zext);
@@ -265,9 +276,13 @@
   EXPECT_EQ(Bonus, Ref);
   EXPECT_TRUE(Bonus > 0);
 
-  // gep + load
-  Ref = getInstCost(Gep) + getInstCost(Load);
+  // gep + load + freeze + smax
+  Ref = getInstCost(Gep) + getInstCost(Load) + getInstCost(Freeze) +
+        getInstCost(Smax);
   Bonus = Specializer.getSpecializationBonus(F->getArg(2), GV, Visitor);
   EXPECT_EQ(Bonus, Ref);
   EXPECT_TRUE(Bonus > 0);
+
+  Bonus = Specializer.getSpecializationBonus(F->getArg(3), Undef, Visitor);
+  EXPECT_TRUE(Bonus == 0);
 }