diff --git a/loopy/preprocess.py b/loopy/preprocess.py
index 741f828e263050b4865f1eff85b3870c9eb2ce9b..01eeb513046be661646d440d7f3a5e7d691ae1b6 100644
--- a/loopy/preprocess.py
+++ b/loopy/preprocess.py
@@ -2166,7 +2166,7 @@ class ArgDescriptionInferer(CombineMapper):
 
     def combine(self, values):
         import operator
-        return reduce(operator.or_, values, set())
+        return reduce(operator.or_, values, frozenset())
 
     def map_call(self, expr, **kwargs):
         from loopy.kernel.function_interface import ValueArgDescriptor
@@ -2200,7 +2200,9 @@ class ArgDescriptionInferer(CombineMapper):
                     combined_arg_id_to_dtype))
 
         # collecting the descriptors for args, kwargs, assignees
-        return set(((expr, new_scoped_function),))
+        return (
+                frozenset(((expr, new_scoped_function), )) |
+                self.combine((self.rec(child) for child in expr.parameters)))
 
     def map_call_with_kwargs(self, expr, **kwargs):
         from loopy.kernel.function_intergace import ValueArgDescriptor
@@ -2234,14 +2236,17 @@ class ArgDescriptionInferer(CombineMapper):
                     combined_arg_id_to_descr))
 
         # collecting the descriptors for args, kwargs, assignees
-        return set(((expr, new_scoped_function),))
+        return (
+                frozenset(((expr, new_scoped_function), )) |
+                self.combine((self.rec(child) for child in expr.parameters)))
 
     def map_constant(self, expr):
-        return set()
+        return frozenset()
 
     map_variable = map_constant
     map_function_symbol = map_constant
 
+
 def infer_arg_descr(kernel):
     """ Specializes the kernel functions in way that the functions agree upon
     shape and dimensions of the arguments too.
@@ -2259,8 +2264,8 @@ def infer_arg_descr(kernel):
                     arg_description_modifier(insn.expression,
                         assignees=insn.assignees))
         if isinstance(insn, (MultiAssignmentBase, CInstruction)):
-            pymbolic_calls_to_functions.update(arg_description_modifier(
-                insn.expression))
+            a = arg_description_modifier(insn.expression)
+            pymbolic_calls_to_functions.update(a)
         elif isinstance(insn, _DataObliviousInstruction):
             pass
         else: