Details

sample5.8m (38.3%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67065×body1280valid
40.4s17266×body2560valid
24.8s42459×body640valid
13.4s13136×body10240exit
10.5s93630×body80valid
9.7s20634×body320valid
7.1s63853×body80nan
2.3s10812×body160valid
1.8s47482×pre80true
1.6s461×body5120valid
766.0ms670×body1280nan
694.0ms702×body640nan
155.0ms377×body320nan
86.0ms198×body160nan

simplify5.4m (35.7%)

prune1.8m (12.1%)

series1.5m (9.9%)

Calls

365 calls:

21.0s
(pow (exp (* (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))))
2.6s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* b eps)))))
2.3s
(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
1.9s
(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
1.1s
(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

rewrite20.6s (2.3%)

Algorithm
120×rewrite-expression-head
Calls

365 calls:

515.0ms
(+ (/ 2.0 (pow x 5)) (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 7))))
454.0ms
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))
418.0ms
(* (/ (exp x) (- (pow (exp x) 3) (pow 1.0 3))) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0))))
305.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
294.0ms
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
Rules
11612×*-un-lft-identity
11196×times-frac
10945×add-sqr-sqrt
8458×add-cube-cbrt
6042×prod-diff
2508×sqrt-prod
1074×add-exp-log
1044×difference-of-squares
841×distribute-lft-out--
803×add-cbrt-cube
761×div-inv
736×distribute-lft-out
718×associate--r+
642×unpow-prod-down
630×add-log-exp
627×fma-neg
619×pow1
523×associate-/r/
476×associate-*l*
444×associate-/l*
441×cbrt-prod
439×associate-/r*
376×associate-*r*
359×log-prod
357×log1p-expm1-u
356×expm1-log1p-u
297×cube-prod
287×flip-- flip3--
280×distribute-rgt-neg-in
279×div-exp
278×sqr-pow
257×distribute-rgt-in distribute-lft-in
213×distribute-lft-neg-in
195×prod-exp
190×fma-def
185×flip-+ flip3-+
165×cbrt-undiv
158×log-pow
157×unswap-sqr associate-+r+
122×exp-sum
112×sqrt-div
107×diff-log cbrt-unprod
102×sub-neg
77×unpow2
73×clear-num frac-2neg
71×pow-unpow
67×neg-mul-1
65×associate-/l/
60×unpow3 cube-mult
56×swap-sqr
54×exp-prod
47×pow-prod-down
45×pow1/3
44×pow-to-exp pow-exp log-div
43×sqrt-pow1
42×pow1/2
40×associate-*l/ 1-exp
39×rec-exp cbrt-div associate-*r/
38×tan-quot
37×*-commutative
33×frac-sub
32×sum-log
30×frac-times
29×frac-add
28×rem-sqrt-square
27×div-sub
21×associate-+l+
20×exp-diff neg-sub0 rem-log-exp
19×fma-udef +-commutative
16×pow-pow
13×complex-mul-def associate--l+
12×cube-div pow-flip
11×associate--l-
10×neg-log inv-pow
rem-exp-log pow-prod-up
difference-cubes exp-neg
distribute-neg-in pow-sqr exp-to-pow
expm1-log1p expm1-udef
rem-cube-cbrt un-div-inv log1p-udef associate-+r- log1p-expm1 *.c-commutative associate-+l- sin-mult
pow2 +.c-commutative pow-plus distribute-frac-neg hypot-def distribute-rgt-out-- rem-cbrt-cube
sin-sum complex-add-def cos-sum tan-sum
associate-+l+.c sin-cos-mult sqrt-unprod distribute-lft-neg-out associate--r- diff-atan sub-div diff-cos hypot-udef rem-square-sqrt distribute-rgt-out associate-*l*.c sqrt-undiv diff-sin

regimes7.2s (0.8%)

Accuracy

Total 28.9b remaining (18.3%)

Threshold costs 5.9b (3.7%)

5.1b82.7%quadp (p42, positive)
4.5b84.1%quadm (p42, negative)
4.5b84.1%quad2m (problem 3.2.1, negative)
3.3b0%expq3 (problem 3.4.2)
2.0b76.4%2nthrt (problem 3.4.6)

localize5.8s (0.6%)

bsearch2.7s (0.3%)

end1.0ms (0.0%)