Details

simplify4.8m (42.8%)

sample4.4m (38.6%)

Algorithm
56×intervals
16×halfpoints
Results
50.7s66434×body1280valid
31.1s17570×body2560valid
17.2s42331×body640valid
9.8s12514×body10240exit
9.1s94134×body80valid
7.2s20864×body320valid
6.4s63446×body80nan
2.9s10327×body160valid
1.1s47417×pre80true
997.0ms671×body1280nan
407.0ms663×body640nan
359.0ms492×body5120valid
115.0ms377×body320nan
96.0ms198×body160nan

prune55.1s (8.1%)

series43.1s (6.3%)

Calls

382 calls:

2.3s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (+ (* eps b) (/ (* (* eps b) (* eps b)) 2)) (* (* 1/6 b) (* eps (* (* eps b) (* eps b)))))))
643.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (* (* (cbrt (pow (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))) (/ 1.0 n))) (cbrt (pow (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))) (/ 1.0 n)))) (cbrt (pow (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))) (/ 1.0 n))))))
642.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))
630.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
607.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))) (/ 1.0 n))))

rewrite16.7s (2.5%)

Algorithm
120×rewrite-expression-head
Calls

382 calls:

2.3s
(cbrt (* (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (* (cos x) (cos x)) (* (cos x) (cos x)))) (cos x)))
489.0ms
(* (* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2)))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2))))
414.0ms
(* (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))))
363.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
361.0ms
(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* x a) (* (* x a) (* (* x a) 1/2))))
Rules
2557×*-un-lft-identity
2505×add-sqr-sqrt
1599×pow1
1498×times-frac
1449×add-cube-cbrt
1196×add-exp-log
1119×add-cbrt-cube
639×add-log-exp
425×pow-prod-down
399×sqrt-prod
389×associate-*l*
387×associate-*r*
375×prod-exp
371×difference-of-squares
347×cbrt-unprod
336×distribute-lft-out--
320×associate-*l/
298×cbrt-div
297×pow-prod-up
278×cbrt-prod
267×flip3-- flip--
265×associate-/l*
254×sqrt-div
241×distribute-lft-out
231×flip-+ flip3-+
223×frac-times
203×log-prod
183×associate-*r/
175×associate-/r*
146×div-exp
133×cbrt-undiv
129×pow-sqr
127×pow-unpow
124×unswap-sqr
122×div-inv
119×pow1/3
112×associate-/r/
110×pow-plus
105×sub-neg
101×diff-log
96×exp-prod
95×log-pow
86×*-commutative
76×associate-/l/
73×unpow-prod-down
69×sqrt-pow1
67×pow2
58×swap-sqr
55×frac-2neg clear-num pow-pow
45×frac-add
39×distribute-rgt-in pow1/2 distribute-lft-in
38×cos-mult
36×sum-log sqr-pow
33×associate-+r+
30×log-div
27×div-sub
24×+-commutative
23×cube-unmult
22×rem-sqrt-square
21×pow-exp frac-sub distribute-rgt-neg-in
20×associate-+l+
19×rem-log-exp
16×cube-prod associate--l+
14×pow3 associate--r+ complex-mul-def pow-to-exp
13×tan-quot
9×distribute-rgt-out--
8×associate--l- distribute-neg-in
7×sub-div
6×exp-diff 1-exp rec-exp
5×neg-sub0 exp-sum neg-log sum-cubes exp-to-pow rem-exp-log cos-sum
4×sqrt-unprod distribute-neg-frac associate-+l- distribute-lft-neg-in
3×sin-sum unpow-prod-up *.c-commutative distribute-frac-neg +.c-commutative sqr-cos
2×associate-+r- distribute-rgt-neg-out sin-mult frac-2neg.c difference-cubes un-div-inv tan-sum complex-add-def associate-*l*.c rem-cbrt-cube pow-sub
1×distribute-lft-neg-out diff-atan rem-cube-cbrt sin-cos-mult unpow1/2 sub0-neg unpow3 neg-mul-1 cube-mult +-inverses diff-sin rem-square-sqrt associate-+l+.c diff-cos e-exp-1

regimes5.7s (0.8%)

Accuracy

Total 21.9b remaining (17.7%)

Threshold costs 7.0b (5.6%)

4.5b84.3%quadp (p42, positive)
4.5b84.3%quad2p (problem 3.2.1, positive)
2.6b90.1%quad2m (problem 3.2.1, negative)
2.3b73.8%2nthrt (problem 3.4.6)
1.0b95.8%quadm (p42, negative)

localize5.1s (0.8%)

bsearch1.4s (0.2%)

end1.0ms (0.0%)