Details

simplify16.4m

Calls

12258 calls:

Slowest
1.7s
(/ (* (* (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (* (* (* (* (+ x 1) x) (- x 1)) (* (* (+ x 1) x) (- x 1))) (* (* (+ x 1) x) (- x 1))))
1.5s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
1.5s
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (/ (* (* (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
1.4s
(/ (* (* (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (* (* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* x x) x)) (* (* (- x 1) (- x 1)) (- x 1))))
1.3s
(/ (* (* 1 1) 1) (/ (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))) (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x)))))

sample4.9m

Algorithm
56×intervals
16×halfpoints
Results
1.1m67225×body1280valid
39.6s17016×body2560valid
26.3s42232×body640valid
13.6s12655×body10240exit
10.6s93909×body80valid
8.5s20460×body320valid
6.8s63978×body80nan
3.0s10889×body160valid
1.9s47284×pre80true
733.0ms668×body1280nan
569.0ms410×body320nan
537.0ms691×body640nan
416.0ms456×body5120valid
45.0ms164×body160nan

prune2.4m

series35.8s

Calls

376 calls:

Slowest
1.3s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
987.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
471.0ms
(log (- 1 (* (* x x) x)))
465.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
443.0ms
(cbrt (* (cbrt x) (cbrt x)))

rewrite15.2s

Algorithm
114×rewrite-expression-head
Calls

376 calls:

Slowest
1.8s
(/ (- (* -1/3 (pow x 9)) (+ (* x (* x x)) (* (* (* (* x x) (* x x)) (* x x)) 1/2))) (log (+ x 1)))
1.3s
(+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))
877.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
371.0ms
(* (* (* (* x x) (* x x)) (* x x)) 1/360)
209.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
Rules
6105×times-frac
5622×*-un-lft-identity
4671×add-sqr-sqrt
3638×add-cube-cbrt
3488×sqrt-prod
1649×add-exp-log
1493×pow1
1448×add-cbrt-cube
751×distribute-lft-out
695×associate-*l*
637×add-log-exp
566×prod-exp
498×cbrt-unprod
481×associate-/l*
461×pow-prod-down
423×associate-*r*
364×insert-posit16
347×difference-of-squares
336×flip3-- flip--
303×div-exp
301×associate-/r*
295×div-inv
283×frac-times
263×associate-*l/
262×distribute-lft-out--
230×cbrt-undiv
206×log-prod
199×associate-*r/
187×flip-+ flip3-+
180×sqrt-div
172×pow-prod-up
170×frac-sub
167×associate-/r/
166×sqrt-pow1
154×pow-unpow
148×swap-sqr
146×associate-/l/
130×unswap-sqr
123×exp-neg
118×pow1/2
117×neg-sub0
114×distribute-rgt-neg-in
112×exp-diff
106×exp-prod pow-sqr
95×sub-neg
93×distribute-lft-neg-in
92×*-commutative
91×cbrt-prod
87×diff-log
86×unpow-prod-down
72×cbrt-div
69×frac-2neg clear-num
68×pow-plus
58×sum-log tan-quot
54×log-pow
47×pow-flip
44×pow2 frac-add log-div
40×1-exp rec-exp
38×distribute-rgt-in distribute-lft-in
35×+-commutative
34×rem-sqrt-square
33×sqr-pow
30×pow1/3
29×difference-of-sqr-1
26×associate-+r+
23×associate-+l+
22×associate--l+ rem-log-exp
21×neg-mul-1
20×div-sub
19×un-div-inv cube-prod
18×inv-pow
16×pow-div exp-sum
13×complex-mul-def
12×associate-+l-
11×pow-exp pow-pow pow-to-exp
10×sin-mult
associate--r+
associate--l- sqrt-unprod distribute-rgt-out--
neg-log
sin-cos-mult
sin-sum distribute-lft1-in cube-mult distribute-rgt-out
distribute-frac-neg sum-cubes
*.c-commutative log-rec sub-div sqr-sin +.c-commutative rem-exp-log rem-square-sqrt
associate-*l*.c associate-+r- tan-sum frac-2neg-c distribute-neg-frac cos-sum complex-add-def
diff-atan rem-cube-cbrt sub0-neg pow3 unpow3 diff-sin associate-+l+.c diff-cos unsub-neg associate--r-

localize4.6s

regimes4.5s

Accuracy

Total 21.5b remaining (19.6%)

4.5b83.7%quad2p (problem 3.2.1, positive)
3.1b87.9%quadm (p42, negative)
3.0b0%expq3 (problem 3.4.2)
2.6b90.1%quad2m (problem 3.2.1, negative)
1.4b84.7%2nthrt (problem 3.4.6)

bsearch1.6s

end14.0ms