;;;; Test input for functions that put simple
;;;; expressions in normal form.
;;;;
;;;; File:         normal-x.in
;;;; Author:       CS 51 (Bob Walton)
;;;; Version:      3

(load "normal-x.lsp")
--->
;; Loading file normal-x.lsp ...
;; Loading of file normal-x.lsp is finished.
T

(normal-1 '(+ (+ x y) z))
--->
(+ X (+ Y Z))

(normal-1 '(+ (+ w x) (+ y z)))
--->
(+ W (+ X (+ Y Z)))

(normal-1 '(+ (+ (+ (+ (+ u v) w) x) y) z))
--->
(+ U (+ V (+ W (+ X (+ Y Z)))))

(normal-1 '(+ (+ (+ (+ (+ (+ u a) v) b) w) c) x))
--->
(+ A (+ B (+ C (+ U (+ V (+ W X))))))

(time (normal-1 '(+ (+ (+ (+ u a) v) b) w)))
--->

Real time: 0.006829f0 sec.
Run time: 0.006832f0 sec.
Space: 3552 Bytes
(+ A (+ B (+ U (+ V W))))



(time (normal-1
       '(+ (+ (+ (+ (+ (+ u a) v) b) w) c) x)))
--->

Real time: 0.051704f0 sec.
Run time: 0.051728f0 sec.
Space: 26208 Bytes
(+ A (+ B (+ C (+ U (+ V (+ W X))))))

(time (normal-1
       '(+ (+ (+ (+ (+ (+ (+ (+ u a) v) b) w)
       			c) x) d) y)))
--->

Real time: 0.319984f0 sec.
Run time: 0.319152f0 sec.
Space: 155232 Bytes
(+ A (+ B (+ C (+ D (+ U (+ V (+ W (+ X Y))))))))

(time (normal-1
       '(+ (+ (+ (+ (+ (+ (+ (+ (+ (+ u a) v) b) w)
       			c) x) d) y) e) z)))
--->

Real time: 2.196511f0 sec.
Run time: 1.778272f0 sec.
Space: 826464 Bytes
GC: 1, GC time: 0.005856f0 sec.
(+ A
  (+ B (+ C (+ D (+ E (+ U (+ V (+ W (+ X (+ Y Z))))))))
) )



(setf *trace* t)
--->
T

(rr-time (normal-2 '(+ (+ (+ x a) y) b)))
--->
((+ X A) => (+ A X))
((+ X A) => (+ A X))
((+ (+ A X) Y) => (+ A (+ X Y)))
((+ X A) => (+ A X))
((+ X A) => (+ A X))
((+ (+ A X) Y) => (+ A (+ X Y)))
((+ (+ A (+ X Y)) B) => (+ A (+ (+ X Y) B)))
((+ (+ X Y) B) => (+ X (+ Y B)))
((+ Y B) => (+ B Y))
((+ Y B) => (+ B Y))
((+ X (+ B Y)) => (+ B (+ X Y)))
((+ (+ X Y) B) => (+ X (+ Y B)))
((+ Y B) => (+ B Y))
((+ Y B) => (+ B Y))
((+ X (+ B Y)) => (+ B (+ X Y)))

Real time: 0.00391f0 sec.
Run time: 0.003904f0 sec.
Space: 28200 Bytes

Number of Rewrites: 15
Number of failures to find any rewrite: 106

(+ A (+ B (+ X Y)))

(setf *trace* nil)
--->
NIL




(setf *trace* t)
--->
T

(rr-time (normal-3 '(+ (+ (+ x a) y) b)))
--->
((+ X A) => (+ A X))
((+ (+ A X) Y) => (+ A (+ X Y)))
((+ (+ A (+ X Y)) B) => (+ A (+ (+ X Y) B)))
((+ (+ X Y) B) => (+ X (+ Y B)))
((+ Y B) => (+ B Y))
((+ X (+ B Y)) => (+ B (+ X Y)))

Real time: 9.77f-4 sec.
Run time: 9.76f-4 sec.
Space: 12720 Bytes

Number of Rewrites: 6
Number of failures to find any rewrite: 11

(+ A (+ B (+ X Y)))

(setf *trace* nil)
--->
NIL



(rr-time (normal-2 '(+ (+ (+ (+ u a) v) b) w)))
--->

Real time: 0.008798f0 sec.
Run time: 0.008784f0 sec.
Space: 6336 Bytes

Number of Rewrites: 37
Number of failures to find any rewrite: 298

(+ A (+ B (+ U (+ V W))))

(rr-time (normal-3 '(+ (+ (+ (+ u a) v) b) w)))
--->

Real time: 9.77f-4 sec.
Run time: 9.76f-4 sec.
Space: 1728 Bytes

Number of Rewrites: 9
Number of failures to find any rewrite: 16

(+ A (+ B (+ U (+ V W))))



(rr-time (normal-2
       '(+ (+ (+ (+ (+ (+ u a) v) b) w) c) x)))
--->

Real time: 0.070244f0 sec.
Run time: 0.070272f0 sec.
Space: 47040 Bytes
GC: 1, GC time: 0.006832f0 sec.

Number of Rewrites: 265
Number of failures to find any rewrite: 2298

(+ A (+ B (+ C (+ U (+ V (+ W X))))))

(rr-time (normal-3
       '(+ (+ (+ (+ (+ (+ u a) v) b) w) c) x)))
--->

Real time: 0.001951f0 sec.
Run time: 0.001952f0 sec.
Space: 4032 Bytes

Number of Rewrites: 21
Number of failures to find any rewrite: 31

(+ A (+ B (+ C (+ U (+ V (+ W X))))))



(rr-time (normal-2
       '(+ (+ (+ (+ (+ (+ (+ (+ u a) v) b) w)
       			c) x) d) y)))
--->

Real time: 0.397054f0 sec.
Run time: 0.391376f0 sec.
Space: 279744 Bytes

Number of Rewrites: 1553
Number of failures to find any rewrite: 14002

(+ A (+ B (+ C (+ D (+ U (+ V (+ W (+ X Y))))))))

(rr-time (normal-3
       '(+ (+ (+ (+ (+ (+ (+ (+ u a) v) b) w)
       			c) x) d) y)))
--->

Real time: 0.003902f0 sec.
Run time: 0.003904f0 sec.
Space: 7296 Bytes

Number of Rewrites: 38
Number of failures to find any rewrite: 51

(+ A (+ B (+ C (+ D (+ U (+ V (+ W (+ X Y))))))))



(rr-time (normal-2
       '(+ (+ (+ (+ (+ (+ (+ (+ (+ (+ u a) v) b) w)
       			c) x) d) y) e) z)))
--->

Real time: 3.667712f0 sec.
Run time: 2.149152f0 sec.
Space: 1493184 Bytes
GC: 3, GC time: 0.017568f0 sec.

Number of Rewrites: 8225
Number of failures to find any rewrite: 75898

(+ A
  (+ B (+ C (+ D (+ E (+ U (+ V (+ W (+ X (+ Y Z))))))))
) )

(rr-time (normal-3
       '(+ (+ (+ (+ (+ (+ (+ (+ (+ (+ u a) v) b) w)
       			c) x) d) y) e) z)))
--->

Real time: 0.00586f0 sec.
Run time: 0.005856f0 sec.
Space: 11520 Bytes

Number of Rewrites: 60
Number of failures to find any rewrite: 76

(+ A
  (+ B (+ C (+ D (+ E (+ U (+ V (+ W (+ X (+ Y Z))))))))
) )