Details

simplify11.1m

Calls

8961 calls:

Slowest
2.0s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x)))))) (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))) (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))))
1.8s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x)))))) (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))) (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))))
1.6s
(/ (* (* (* eps (- (exp (* (+ a b) eps)) 1)) (* eps (- (exp (* (+ a b) eps)) 1))) (* eps (- (exp (* (+ a b) eps)) 1))) (* (* (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))))
1.5s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x)))))) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))))
1.4s
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* (* x x) (* x x)) (* x x)))

sample5.0m

Algorithm
56×intervals
16×halfpoints
Results
1.1m66803×body1280valid
38.5s17450×body2560valid
27.2s42512×body640valid
14.3s13045×body10240exit
11.8s94061×body80valid
8.8s20359×body320valid
6.8s63239×body80nan
2.7s10698×body160valid
2.0s47566×pre80true
697.0ms623×body1280nan
583.0ms475×body5120valid
525.0ms684×body640nan
170.0ms350×body320nan
79.0ms198×body160nan

prune1.9m

rewrite37.1s

Algorithm
111×rewrite-expression-head
Calls

353 calls:

Slowest
14.1s
(- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))
12.6s
(/ (- (* (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x)))) (+ (* (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1)))) (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (* (cbrt x) (cbrt x))))
351.0ms
(cbrt (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))))))
271.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
236.0ms
(* x (* (* a 1/6) (* (* a x) (* a x))))
Rules
3421×*-un-lft-identity
3090×add-sqr-sqrt
2874×pow1
2718×times-frac
2006×add-cube-cbrt
1437×add-exp-log
1296×add-cbrt-cube
835×pow-prod-up
752×cbrt-prod
713×pow-prod-down
615×add-log-exp
550×sqrt-prod
507×prod-exp
470×associate-*l*
461×cbrt-unprod
438×distribute-lft-out
417×associate-*r*
375×pow-sqr
369×difference-of-squares
360×pow-plus
343×insert-posit16
285×log-prod
265×associate-/l*
243×distribute-lft-out--
231×pow2
226×associate-/r*
218×swap-sqr
216×associate-*l/
211×div-inv
210×frac-times
209×div-exp
204×associate-*r/
177×flip3-- flip--
174×flip-+ flip3-+
171×cbrt-undiv
149×unswap-sqr
144×cbrt-div
139×associate-/r/
136×pow-unpow
100×log-pow
98×unpow-prod-down
96×exp-prod
92×sqrt-div
87×*-commutative
86×sub-neg
83×diff-log
71×associate-/l/
65×distribute-rgt-neg-in
60×sqrt-pow1 frac-2neg clear-num
56×sum-log
55×frac-add
52×pow1/2
47×pow1/3
44×sqr-pow
43×distribute-lft-neg-in
42×log-div
36×+-commutative
31×difference-of-sqr-1
30×distribute-rgt-in distribute-lft-in
26×rem-log-exp 1-exp rec-exp
23×rem-sqrt-square
22×div-sub
21×pow-flip
18×tan-quot
17×exp-sum
16×pow-exp associate--l+ pow-to-exp
15×pow-pow
14×frac-sub
13×complex-mul-def
12×sin-mult
10×neg-sub0 associate--l- associate--r+ inv-pow cube-prod
associate-+l+ neg-mul-1
associate-+r+ neg-log
exp-diff exp-to-pow
cos-mult
sin-sum sqrt-unprod
distribute-frac-neg distribute-lft1-in un-div-inv distribute-rgt-out
*.c-commutative sqr-sin +.c-commutative distribute-rgt-out-- associate-+l- cos-sum cube-mult
associate-*l*.c rem-cube-cbrt sub0-neg pow3 unpow3 sub-div associate-+r- tan-sum rem-exp-log complex-add-def rem-square-sqrt
diff-atan sin-cos-mult cube-unmult sum-cubes distribute-neg-frac sqr-cos associate-+l+.c diff-sin diff-cos exp-lft-cube

series33.7s

Calls

353 calls:

Slowest
1.2s
(log (sqrt (exp (* (* x x) (* x x)))))
667.0ms
(log (sqrt (exp (* (* x x) (* x x)))))
610.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
586.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
458.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))))))))) (tan x))

localize4.8s

bsearch4.2s

regimes3.9s

Accuracy

Total 20.9b remaining (17%)

5.1b78.6%quad2m (problem 3.2.1, negative)
4.4b81%quad2p (problem 3.2.1, positive)
3.1b72.1%2nthrt (problem 3.4.6)
1.4b93.9%quadp (p42, positive)
0.9b96.1%quadm (p42, negative)

end1.0ms