Details

rewrite11.2m (33.2%)

Algorithm
161×rewrite-expression-head
Calls

491 calls:

21.8s
(* (/ (+ (* (* x x) (+ (* (* (* x x) (* (* x x) (* x x))) (+ 0.0005064034 (* (* x x) 0.0001789971))) 0.1049934947)) (+ (+ 1.0 (* (* (* x x) (* x x)) 0.0424060604)) (* 0.0072644182 (* (* x x) (* (* x x) (* x x)))))) (+ (* (* (* (* x x) (* (* x x) (* x x))) (* (* x x) (* x x))) (+ (* (* (* x x) 0.0001789971) 2.0) 0.0008327945)) (+ (* (* x x) (+ (* (* (* x x) (* x x)) (+ (* (* x x) 0.0140005442) 0.0694555761)) (+ 0.7715471019 (* (* x x) 0.2909738639)))) 1.0))) x)
11.2s
(/ (+ (* (* x x) (+ (* (* (* x x) (* (* x x) (* x x))) (+ 0.0005064034 (* (* x x) 0.0001789971))) 0.1049934947)) (+ (+ 1.0 (* (* (* x x) (* x x)) 0.0424060604)) (* 0.0072644182 (* (* x x) (* (* x x) (* x x)))))) (+ (* (* (* (* x x) (* (* x x) (* x x))) (* (* x x) (* x x))) (+ (* (* (* x x) 0.0001789971) 2.0) 0.0008327945)) (+ (* (* x x) (+ (* (* (* x x) (* x x)) (+ (* (* x x) 0.0140005442) 0.0694555761)) (+ 0.7715471019 (* (* x x) 0.2909738639)))) 1.0)))
3.1s
(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))
2.9s
(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))))))
2.9s
(* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)
Rules
25500×frac-times
16274×associate-*r/
12088×times-frac
10062×associate-*l/
8566×*-un-lft-identity
8037×flip-+ flip3-+
7883×exp-neg
7508×frac-add
7453×add-sqr-sqrt
6959×exp-diff
6824×neg-sub0
6197×add-cube-cbrt
3959×pow1
3333×sqrt-prod
2602×add-exp-log
2383×add-cbrt-cube
1583×cbrt-div
1287×pow-prod-up
1215×associate-*r*
1141×associate-*l*
1129×un-div-inv
1100×distribute-lft-out
1054×prod-exp
913×cbrt-unprod
805×pow-prod-down
775×add-log-exp
659×associate-/r/
652×pow-plus
479×div-exp
466×div-inv
410×cbrt-prod
406×associate-/r*
400×cbrt-undiv
377×associate-/l*
337×pow-sqr
325×swap-sqr
287×unswap-sqr
285×difference-of-squares
244×pow2
239×sqrt-div
214×flip3-- flip--
205×associate-+l-
187×log-pow
171×*-commutative
140×sqrt-pow1
138×distribute-lft-out--
132×sum-log
128×unpow-prod-down
112×pow1/2 cube-div
105×pow1/3
94×associate-/l/
90×cube-prod
84×pow-exp
81×log-prod
75×frac-2neg clear-num
70×rem-sqrt-square
67×associate-+r- sqr-pow unsub-neg
60×distribute-rgt-in distribute-lft-in
59×cube-unmult
52×sub-neg
50×+-commutative
39×pow-unpow
38×pow-to-exp diff-log
37×exp-sum 1-exp
29×rem-cube-cbrt pow-pow
26×rec-exp
20×frac-sub
19×exp-prod
18×distribute-rgt-neg-in
14×associate-+r+
13×div-sub distribute-rgt-out
10×pow3 log-div distribute-rgt1-in
9×associate-+l+ unpow3 cube-mult
7×rem-exp-log
6×sin-sum distribute-lft-neg-in associate--r+ rem-log-exp
5×cos-sum
4×pow-flip neg-log inv-pow
3×sqrt-unprod associate--l+
2×sqrt-undiv difference-cubes rem-square-sqrt associate--r-
1×unpow-prod-up sum-cubes neg-mul-1 distribute-rgt-out-- distribute-neg-in rem-cbrt-cube pow-sub

simplify8.8m (26.0%)

series5.1m (15.2%)

Calls

489 calls:

2.6m
(- (pow (pow 1.0 3) 3) (pow (* (sqrt (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3)) (sqrt (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3))) 3))
31.8s
(log (* (exp (* (* 1.0 1.0) 1.0)) (exp (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))))))
21.6s
(* (exp (* (* 1.0 1.0) 1.0)) (exp (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))))))
8.8s
(+ (* (* 1.0 1.0) 1.0) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))))
4.6s
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3))

prune4.4m (13.2%)

sample3.7m (10.9%)

Algorithm
99×intervals
Results
1.3m11978×body10240exit
53.9s454278×body80valid
24.9s27048×body1280valid
14.2s21157×body640valid
6.9s70443×body80nan
4.3s1557×body1280nan
4.3s10846×body320valid
3.1s1342×body640nan
2.5s9639×body160valid
2.2s49536×pre80true
1.4s693×body320nan
1.0s1395×body2560valid
324.0ms616×body5120valid
267.0ms327×body160nan

regimes15.0s (0.7%)

Accuracy

Total 90.8b remaining (32.3%)

Threshold costs 4.1b (1.5%)

13.6b35.4%math.sqrt on complex, real part
10.5b56.7%math.log/2 on complex, real part
10.1b57.9%math.log10 on complex, real part
9.9b58.7%math.log/1 on complex, real part
9.6b58.6%math.abs on complex

localize9.8s (0.5%)

bsearch3.0s (0.2%)

end1.0ms (0.0%)