Explanation for Slow Performance of VARCHAR2 Overloading?

Valentin Nikotin, a PL/SQL Challenge player, recently brought to my attention some unexpectedly slow performance when executing from within a query an overloaded function that accepts a VARCHAR2 argument, compared to a NUMBER argument. I have been able to reproduce this (see below). I thought I'd see if any readers of this blog had an idea as to what might be the cause.

We both ran this code on an 11.2 instance.

CREATE OR REPLACE PACKAGE pkg_test
AS
   FUNCTION fv (i VARCHAR2)
      RETURN NUMBER;

   FUNCTION fn (i NUMBER)
      RETURN NUMBER;
END;
/

CREATE OR REPLACE PACKAGE BODY pkg_test
AS
   FUNCTION fv (i VARCHAR2)
      RETURN NUMBER
   IS
   BEGIN
      RETURN 1;
   END;

   FUNCTION fn (i NUMBER)
      RETURN NUMBER
   IS
   BEGIN
      RETURN 1;
   END;
END;
/

CREATE OR REPLACE FUNCTION fv (i VARCHAR2)
   RETURN NUMBER
IS
BEGIN
   RETURN 1;
END;
/

CREATE OR REPLACE FUNCTION fn (i NUMBER)
   RETURN NUMBER
IS
BEGIN
   RETURN 1;
END;
/

/* No difference in PL/SQL 

"VC2 overloading" completed in: 2.5 seconds
"Number overloading" completed in: 2.52 seconds
"Schema-level VC2" completed in: 2.48 seconds
"Schema-level Number" completed in: 2.49 seconds

*/

DECLARE
   l             NUMBER;
   last_timing   NUMBER := NULL;

   PROCEDURE start_timer
   IS
   BEGIN
      last_timing := DBMS_UTILITY.get_cpu_time;
   END;

   PROCEDURE show_elapsed_time (message_in IN VARCHAR2 := NULL)
   IS
   BEGIN
      DBMS_OUTPUT.put_line (
            '"'
         || message_in
         || '" completed in: '
         || (DBMS_UTILITY.get_cpu_time - last_timing) / 100
         || ' seconds');
   END;
BEGIN
   start_timer;

   FOR indx IN 1 .. 10000000
   LOOP
      l := pkg_test.fv (NULL);
   END LOOP;

   show_elapsed_time ('VC2 overloading');
   --
   start_timer;

   FOR indx IN 1 .. 10000000
   LOOP
      l := pkg_test.fn (NULL);
   END LOOP;

   show_elapsed_time ('Number overloading');
   --
   start_timer;

   FOR indx IN 1 .. 10000000
   LOOP
      l := fv (NULL);
   END LOOP;

   show_elapsed_time ('Schema-level VC2');
   --
   start_timer;

   FOR indx IN 1 .. 10000000
   LOOP
      l := fv (NULL);
   END LOOP;

   show_elapsed_time ('Schema-level Number');
END;
/

/* Noticeable difference in SQL 

MAX(PKG_TEST.FV(NULL))
----------------------
                     1
1 row selected.
Elapsed: 00:00:07.93

MAX(FV(NULL))
-------------
            1
1 row selected.
Elapsed: 00:00:05.03

MAX(PKG_TEST.FN(NULL))
----------------------
                     1
1 row selected.
Elapsed: 00:00:04.45

MAX(FN(NULL))
-------------
            1
1 row selected.
Elapsed: 00:00:05.45

*/

SET TIMING ON

CREATE TABLE driver_table
AS
       SELECT LEVEL id
         FROM DUAL
   CONNECT BY LEVEL < 1000000
/

SELECT MAX (pkg_test.fv (NULL)) FROM driver_table
/

SELECT MAX (fv (NULL)) FROM driver_table
/

SELECT MAX (pkg_test.fn (NULL)) FROM driver_table
/

SELECT MAX (fn (NULL)) FROM driver_table
/

DROP driver_table
/

DROP package pkg_test
/

DROP FUNCTION fn
/

DROP FUNCTION fv
/