Details

simplify10.9m (53.6%)

sample5.2m (25.5%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66984×body1280valid
41.4s17605×body2560valid
27.1s41893×body640valid
15.6s12712×body10240exit
12.0s93924×body80valid
8.5s20786×body320valid
6.9s64007×body80nan
2.8s10563×body160valid
2.1s47357×pre80true
767.0ms680×body1280nan
620.0ms696×body640nan
464.0ms463×body5120valid
161.0ms359×body320nan
53.0ms192×body160nan

prune3.3m (16.2%)

series36.3s (3.0%)

Calls

347 calls:

573.0ms
(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
546.0ms
(fma (/ (sin x) (* (cos x) (cos x))) (/ (/ (sin x) x) x) (- (- (/ (/ (sin x) x) (cos x)) (/ (sin x) x)) (* (/ (/ (sin x) x) (cos x)) (/ (sin x) x))))
485.0ms
(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
473.0ms
(/ (* x (fma (* (* (* x x) 1/45) (* (* x x) 1/45)) (* (* x x) 1/45) 1/27)) (+ (* (* x (* x 1/45)) (* x (* x 1/45))) (- (* 1/3 1/3) (* (* x (* x 1/45)) 1/3))))
460.0ms
(cbrt (cbrt x))

rewrite10.7s (0.9%)

Algorithm
115×rewrite-expression-head
Calls

347 calls:

506.0ms
(+ (+ (+ (/ 1/2 n) (+ 1 (log n))) (/ -1/6 (* n n))) -1)
462.0ms
(cbrt (* (* (* (* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x)))) (* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x))))) (* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x))))) (expm1 (* a x))))
366.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
218.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
206.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
Rules
9780×*-un-lft-identity
9704×times-frac
8494×add-sqr-sqrt
7183×add-cube-cbrt
4596×prod-diff
2728×pow1
2710×sqrt-prod
1081×add-exp-log
1012×add-cbrt-cube
928×distribute-lft-out
879×pow-prod-up
646×div-inv
545×add-log-exp
539×unpow-prod-down
525×difference-of-squares
518×pow-prod-down
506×associate-+l+
455×fma-neg
414×distribute-lft-out--
413×associate-/r*
399×associate-/r/
389×pow-sqr
387×associate-/l*
356×pow-plus
348×log1p-expm1-u
341×expm1-log1p-u
340×insert-posit16
321×associate-*l*
276×prod-exp
268×cbrt-unprod associate-*r*
251×pow2
225×flip-+ flip3-+
200×flip3-- flip--
195×cbrt-prod
190×div-exp log-prod
180×sqr-pow
157×cbrt-undiv associate-*l/
131×distribute-rgt-neg-in
122×sqrt-div
111×distribute-lft-neg-in
100×fma-def
98×unswap-sqr
85×frac-times
83×diff-log
81×sub-neg
77×exp-sum
69×*-commutative
67×frac-2neg clear-num
66×associate-/l/
60×log-pow
59×associate-*r/
58×swap-sqr
56×sqrt-pow1
53×pow1/2
50×distribute-rgt-in distribute-lft-in frac-add
44×tan-quot
43×cbrt-div
39×pow-unpow
38×pow1/3
37×neg-mul-1
34×rem-sqrt-square
33×exp-prod
30×sum-log
25×pow-flip
24×hypot-def
22×div-sub fma-udef
20×1-exp rec-exp
18×associate--l+ +-commutative log-div
15×frac-sub inv-pow
12×associate--r+ rem-log-exp
11×difference-of-sqr-1 log1p-udef
10×associate--l-
9×expm1-udef sin-mult
8×expm1-log1p neg-sub0 pow-div
7×exp-diff
6×cos-mult neg-log rem-exp-log
5×pow3 distribute-rgt-out-- associate-+l-
4×log1p-def pow-exp sub-div pow-to-exp
3×cube-unmult log1p-expm1 sqrt-unprod sqr-sin pow-pow cos-sum rem-cbrt-cube
2×sin-sum +.c-commutative un-div-inv tan-sum exp-neg
1×diff-atan frac-2neg.c sin-cos-mult exp-to-pow rem-square-sqrt sqr-cos +-inverses diff-sin diff-cos expm1-def difference-of-sqr--1

regimes4.9s (0.4%)

Accuracy

Total 21.1b remaining (14.9%)

Threshold costs 4.1b (2.9%)

5.6b79.9%quadm (p42, negative)
4.3b84.5%quad2p (problem 3.2.1, positive)
3.1b0%expq3 (problem 3.4.2)
1.5b86.7%2nthrt (problem 3.4.6)
1.3b79.5%quadp (p42, positive)

localize4.4s (0.4%)

bsearch1.0s (0.1%)

end2.0ms (0.0%)