Details

simplify8.1m (44.9%)

sample5.0m (27.9%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67054×body1280valid
38.4s16738×body2560valid
27.3s42949×body640valid
13.2s12797×body10240exit
12.2s93858×body80valid
9.4s20341×body320valid
7.3s63262×body80nan
2.8s10547×body160valid
2.2s47451×pre80true
948.0ms664×body1280nan
534.0ms456×body5120valid
529.0ms660×body640nan
172.0ms371×body320nan
54.0ms193×body160nan

prune3.8m (21.4%)

series40.7s (3.8%)

Calls

345 calls:

1.2s
(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
902.0ms
(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
794.0ms
(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
789.0ms
(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
763.0ms
(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite10.4s (1.0%)

Algorithm
113×rewrite-expression-head
Calls

345 calls:

533.0ms
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
448.0ms
(* x (- (* (* x (* x 1/45)) (* x (* x 1/45))) (* 1/3 1/3)))
285.0ms
(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
264.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
245.0ms
(* (+ (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt (+ x 1))))))
Rules
14797×times-frac
14454×*-un-lft-identity
12361×add-sqr-sqrt
10695×add-cube-cbrt
8969×sqrt-prod
7963×prod-diff
1906×pow1
1377×distribute-lft-out
1258×distribute-rgt-in distribute-lft-in
1152×add-exp-log
1066×div-inv
1002×add-cbrt-cube
722×associate-/r/
587×difference-of-squares
537×pow-prod-up
498×add-log-exp
484×associate-+l+ associate--l+
473×distribute-lft-out--
445×associate-*l*
427×fma-neg
397×associate-*r*
388×associate-/r*
376×cbrt-prod
364×associate-/l*
355×pow-prod-down
347×log1p-expm1-u
338×expm1-log1p-u insert-posit16
322×flip-+ flip3-+
313×sqrt-div
269×prod-exp
244×flip3-- flip--
242×div-exp
240×cbrt-unprod pow-sqr
214×frac-sub
212×pow-plus
190×unpow-prod-down
183×swap-sqr
174×cbrt-undiv
159×sqrt-pow1
147×pow2
143×frac-times
141×unswap-sqr
117×distribute-rgt-neg-in
105×distribute-lft-neg-in
104×associate-*l/
102×pow1/2 associate-/l/
91×associate-*r/
87×fma-def
80×frac-2neg clear-num
72×sub-neg
67×pow-flip sqr-pow *-commutative
65×diff-log
60×log-prod
52×pow1/3
46×inv-pow
44×1-exp rec-exp
39×rem-sqrt-square
37×frac-add
36×difference-of-sqr-1
35×neg-mul-1
32×un-div-inv
30×cbrt-div
28×tan-quot
27×log-pow
26×pow-unpow
24×fma-udef
21×sum-log div-sub exp-prod
14×+-commutative hypot-def
11×expm1-udef
9×expm1-log1p
7×neg-sub0 associate--l- rem-log-exp
6×associate--r+ log-div
5×pow-exp neg-log sqrt-unprod pow-to-exp associate-+l- log1p-udef
4×pow-div cube-unmult pow3 sin-mult
3×log1p-expm1 sqr-sin rem-square-sqrt rem-cbrt-cube
2×quot-tan exp-diff sin-sum associate-+r+ +.c-commutative pow-pow tan-sum exp-neg log1p-def cos-sum expm1-def
1×diff-atan cos-mult sqrt-undiv frac-2neg.c sin-cos-mult exp-sum hypot-udef distribute-rgt-out-- rem-exp-log +-inverses diff-sin diff-cos difference-of-sqr--1

localize4.6s (0.4%)

regimes4.3s (0.4%)

Accuracy

Total 19.2b remaining (13.7%)

Threshold costs 4.9b (3.5%)

4.7b83%quad2p (problem 3.2.1, positive)
4.1b84.7%quadm (p42, negative)
2.8b15.8%expq3 (problem 3.4.2)
1.5b87.3%2nthrt (problem 3.4.6)
1.3b94.5%quad2m (problem 3.2.1, negative)

bsearch2.1s (0.2%)

end1.0ms (0.0%)