Details

simplify4.6m (38.6%)

sample4.4m (36.5%)

Algorithm
56×intervals
16×halfpoints
Results
51.8s66591×body1280valid
31.6s17465×body2560valid
18.0s42320×body640valid
11.1s13110×body10240exit
8.5s93621×body80valid
6.5s20970×body320valid
5.1s63689×body80nan
2.8s10714×body160valid
1.5s47471×pre80true
563.0ms658×body1280nan
410.0ms647×body640nan
365.0ms454×body5120valid
185.0ms407×body320nan
35.0ms178×body160nan

prune1.7m (14.0%)

series51.6s (7.2%)

Calls

378 calls:

906.0ms
(fma (- (cbrt (/ 1.0 (sqrt (+ x 1.0))))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (cbrt (/ 1.0 (sqrt (+ x 1.0))))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (cbrt (/ 1.0 (sqrt (+ x 1.0)))))))
866.0ms
(log (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
708.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
655.0ms
(fma (- (/ 1.0 (sqrt (cbrt (+ x 1.0))))) (/ 1 (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (* (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (/ 1 (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))))
564.0ms
(/ (fma (exp x) (- (exp (fma 2 x x)) (* 2.0 (* 2.0 2.0))) (fma (exp x) (exp x) (* 2.0 (+ (exp x) 2.0)))) (* (fma (exp x) (exp x) (* 2.0 (+ (exp x) 2.0))) (exp x)))

rewrite12.6s (1.7%)

Algorithm
121×rewrite-expression-head
Calls

378 calls:

356.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
285.0ms
(log (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
273.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
247.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
178.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (sqrt (+ x 1.0)) (sqrt x)))
Rules
12145×*-un-lft-identity
11630×times-frac
10479×add-sqr-sqrt
8616×add-cube-cbrt
5743×prod-diff
4841×sqrt-prod
1401×pow1
1188×distribute-lft-out
985×add-exp-log
887×add-cbrt-cube
771×difference-of-squares
726×unpow-prod-down
680×div-inv
655×distribute-lft-out--
620×add-log-exp
584×associate-/r/
544×fma-neg
490×associate-/l*
368×expm1-log1p-u
367×log1p-expm1-u
365×pow-prod-up
360×cbrt-prod
343×associate-*l*
342×sqrt-div
334×associate-/r*
287×flip-+ flip3-+
274×associate-*r*
263×flip3-- flip--
259×log-prod
248×associate-+l+
242×sqr-pow pow-plus distribute-rgt-neg-in
227×pow-prod-down
220×distribute-lft-neg-in
201×div-exp
186×prod-exp
177×cbrt-unprod fma-def
174×exp-sum
170×cbrt-div
152×cbrt-undiv
141×log-pow
135×pow-sqr
125×exp-prod
105×frac-times
101×diff-log
96×unswap-sqr sub-neg
95×associate-+r+
91×associate-*r/
81×pow2
79×pow1/3
78×swap-sqr
76×frac-2neg clear-num
73×neg-mul-1
71×associate-*l/
62×distribute-rgt-in distribute-lft-in
57×associate-/l/
52×pow-unpow
51×*-commutative
44×sqrt-pow1 pow1/2
40×fma-udef
33×rem-sqrt-square log-div
29×div-sub
27×tan-quot pow3
25×sum-log
19×rem-log-exp hypot-def
18×exp-diff
16×1-exp rec-exp +-commutative frac-add
14×neg-sub0 complex-mul-def
13×frac-sub
11×associate--l- associate--l+
pow-exp neg-log pow-to-exp
quot-tan rem-exp-log
associate--r+
distribute-neg-frac
associate-+r- exp-to-pow
pow-flip distribute-frac-neg pow-pow inv-pow
*.c-commutative +.c-commutative distribute-rgt-out--
expm1-udef associate-*l*.c sin-sum cube-unmult sqrt-unprod tan-sum exp-neg associate-+l- rem-square-sqrt cos-sum rem-cbrt-cube distribute-neg-in unsub-neg pow-div complex-add-def
diff-atan cos-mult frac-2neg.c sin-cos-mult distribute-rgt-neg-out log1p-expm1 sin-mult sub-div un-div-inv diff-sin associate-+l+.c exp-lft-cube diff-cos log1p-udef

regimes6.7s (0.9%)

Accuracy

Total 30.8b remaining (18.6%)

Threshold costs 7.1b (4.3%)

4.9b85.5%quadp (p42, positive)
4.7b85.9%quad2p (problem 3.2.1, positive)
3.9b86.6%quad2m (problem 3.2.1, negative)
3.8b86.6%quadm (p42, negative)
3.1b0%expq3 (problem 3.4.2)

localize5.7s (0.8%)

bsearch1.8s (0.3%)

end1.0ms (0.0%)