Index: llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
===================================================================
--- llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
+++ llvm/lib/Transforms/IPO/FunctionSpecialization.cpp
@@ -677,8 +677,12 @@
       auto *V = CS.getArgOperand(A->getArgNo());
       if (isa<PoisonValue>(V))
         return false;
-      if (isa<ConstantExpr>(V))
-        return false;
+
+      // For now, constant expressions are fine but only if they are function
+      // calls.
+      if (auto *CE =  dyn_cast<ConstantExpr>(V))
+        if (!isa<Function>(CE->getOperand(0)))
+          return false;
 
       // TrackValueOfGlobalVariable only tracks scalar global variables.
       if (auto *GV = dyn_cast<GlobalVariable>(V)) {
Index: llvm/test/Transforms/FunctionSpecialization/function-specialization-constant-expression3.ll
===================================================================
--- llvm/test/Transforms/FunctionSpecialization/function-specialization-constant-expression3.ll
+++ llvm/test/Transforms/FunctionSpecialization/function-specialization-constant-expression3.ll
@@ -4,8 +4,8 @@
 define i32 @main() {
 ; CHECK-LABEL: @main(
 ; CHECK-NEXT:  bb:
-; CHECK-NEXT:    tail call void @wombat(i8* undef, i64 undef, i64 undef, i32 (i8*, i8*)* bitcast (i32 ()* @quux to i32 (i8*, i8*)*))
-; CHECK-NEXT:    tail call void @wombat(i8* undef, i64 undef, i64 undef, i32 (i8*, i8*)* bitcast (i32 ()* @eggs to i32 (i8*, i8*)*))
+; CHECK-NEXT:    tail call void @wombat.1(i8* undef, i64 undef, i64 undef, i32 (i8*, i8*)* bitcast (i32 ()* @quux to i32 (i8*, i8*)*))
+; CHECK-NEXT:    tail call void @wombat.2(i8* undef, i64 undef, i64 undef, i32 (i8*, i8*)* bitcast (i32 ()* @eggs to i32 (i8*, i8*)*))
 ; CHECK-NEXT:    ret i32 undef
 ;
 bb: