Details

simplify7.0m (46.8%)

sample5.0m (33.4%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67063×body1280valid
39.8s17671×body2560valid
28.0s41322×body640valid
13.3s12541×body10240exit
11.3s93881×body80valid
8.9s20662×body320valid
8.5s64155×body80nan
2.8s10837×body160valid
1.9s47390×pre80true
822.0ms724×body1280nan
624.0ms478×body5120valid
600.0ms689×body640nan
187.0ms388×body320nan
49.0ms169×body160nan

prune2.0m (13.4%)

series40.1s (4.5%)

Calls

330 calls:

818.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
816.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
785.0ms
(fma (- (pow (cbrt x) (/ 1 n))) (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
767.0ms
(log (exp (fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))))
740.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite7.1s (0.8%)

Algorithm
112×rewrite-expression-head
Calls

330 calls:

241.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (* (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (/ 1 (cbrt (- x 1)))))
191.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
172.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
132.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
129.0ms
(cbrt (* (* (* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x)))) (* (cbrt (expm1 (* a x))) (expm1 (* a x)))) (expm1 (* a x))))
Rules
8020×*-un-lft-identity
7967×times-frac
7645×add-sqr-sqrt
6293×add-cube-cbrt
4317×prod-diff
2158×pow1
1469×sqrt-prod
933×add-exp-log
908×cbrt-prod
836×add-cbrt-cube
644×pow-prod-up
615×div-inv
503×distribute-lft-out
486×associate-+l+
477×add-log-exp
454×difference-of-squares
416×fma-neg
402×associate-*l*
397×pow-prod-down
360×associate-*r*
329×log1p-expm1-u
324×expm1-log1p-u insert-posit16
311×associate-/r/
304×distribute-lft-out--
297×pow-sqr
280×pow-plus
253×associate-/r*
238×prod-exp
227×cbrt-unprod
194×associate-/l*
191×pow2
184×unpow-prod-down
175×flip-+ flip3-+
168×unswap-sqr
160×swap-sqr
158×distribute-rgt-neg-in
145×flip3-- flip--
134×sqrt-div
133×log-prod
129×div-exp
126×distribute-lft-neg-in
105×pow1/3
104×cbrt-div
99×cbrt-undiv
90×fma-def
77×sqrt-pow1
71×*-commutative
69×pow-unpow
67×associate-*l/
63×sqr-pow
62×sub-neg
61×diff-log
58×associate-*r/
57×pow1/2
51×frac-times
48×frac-2neg clear-num
42×neg-mul-1
41×log-pow
39×fma-udef
37×distribute-rgt-in distribute-lft-in
35×associate-/l/
32×tan-quot
29×rem-sqrt-square
23×difference-of-sqr-1 frac-add
22×pow-flip
21×1-exp rec-exp
20×sum-log div-sub
17×+-commutative
16×frac-sub pow-pow
14×inv-pow
13×log-div
12×associate--l+ exp-prod hypot-def rem-log-exp
10×pow3
pow-exp
neg-sub0 exp-sum associate--l-
un-div-inv pow-to-exp
expm1-udef neg-log associate--r+
expm1-log1p log1p-def
unpow-prod-up sin-mult
log1p-udef sqr-sin associate-+l- rem-cbrt-cube
exp-diff cos-mult sin-sum cube-unmult sqrt-unprod +.c-commutative tan-sum rem-exp-log rem-square-sqrt cos-sum exp-neg
quot-tan diff-atan difference-of-sqr--1 sin-cos-mult log1p-expm1 exp-to-pow hypot-udef sqr-cos diff-sin diff-cos expm1-def e-exp-1

regimes4.2s (0.5%)

Accuracy

Total 22.4b remaining (15.1%)

Threshold costs 4.3b (2.9%)

4.9b82.3%quad2p (problem 3.2.1, positive)
4.5b86.7%quadm (p42, negative)
3.5b0%expq3 (problem 3.4.2)
3.5b89.7%quad2m (problem 3.2.1, negative)
1.7b84.9%2nthrt (problem 3.4.6)

localize4.0s (0.4%)

bsearch2.9s (0.3%)

end1.0ms (0.0%)