Details

rewrite10.1m (35.3%)

Algorithm
163×rewrite-expression-head
Calls

510 calls:

1.2m
(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))
1.1m
(+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))
1.1m
(+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))
56.5s
(* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))
53.1s
(* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (- z 1.0) 7.0))) (* (/ (sqrt (* PI 2.0)) (exp 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))))
Rules
107551×times-frac
57243×*-un-lft-identity
43271×add-sqr-sqrt
41143×add-cube-cbrt
8635×frac-add
7953×distribute-lft-out
7006×sqrt-prod
5458×flip-+ flip3-+
5000×associate-/r/
4357×div-inv
4212×add-exp-log
3409×associate-*r/
2709×frac-times
2535×add-cbrt-cube
2303×associate-*r*
1943×pow1
1880×associate-/l*
1748×div-exp
1384×associate-*l*
1339×prod-exp
1143×difference-of-squares
937×associate-/r*
869×add-log-exp
781×cbrt-unprod
727×unpow-prod-down
680×associate-*l/
645×distribute-lft-out--
639×cbrt-undiv
601×pow-prod-down
565×flip3-- flip--
472×sqrt-div
392×cbrt-prod
343×pow-exp
341×associate-+l-
331×pow-sub
328×unswap-sqr
326×frac-sub
302×log-pow
297×1-exp
254×cbrt-div
252×sqrt-pow1
229×exp-sum
201×rec-exp
190×pow-to-exp
175×sum-log
168×cube-prod
163×*-commutative
154×sub-neg
151×sqr-pow swap-sqr
150×pow1/2
140×associate-/l/
134×distribute-rgt-in distribute-lft-in
102×frac-2neg clear-num
99×log-prod
77×pow1/3
67×pow-prod-up
64×rem-sqrt-square
63×pow-unpow
61×+-commutative
56×unpow-prod-up
45×pow-sqr
44×diff-log
35×exp-prod
33×associate-+r+
31×pow-pow
29×unpow3 cube-mult
25×distribute-rgt-neg-in
24×associate--l+
23×exp-diff
22×pow-plus
20×div-sub
18×cube-div pow2 log-div
16×rem-cube-cbrt
12×associate-+l+ sub-div
11×associate-+r-
10×inv-pow pow-flip rem-log-exp
9×rem-exp-log
8×un-div-inv distribute-lft-neg-in associate--r+
7×exp-to-pow
6×distribute-neg-in
5×sqrt-unprod difference-of-sqr-1 rem-square-sqrt
4×difference-of-sqr--1 neg-sub0 rem-cbrt-cube
3×sin-sum unpow2
2×pow-div sqrt-undiv unsub-neg neg-mul-1
1×cos-sum difference-cubes sqrt-pow2 pow3 distribute-rgt-out-- associate--r-

simplify8.0m (27.7%)

prune4.8m (16.7%)

sample3.9m (13.5%)

Algorithm
100×intervals
Results
1.1m496506×body80valid
1.0m15777×body10240exit
32.5s30244×body1280valid
15.4s23335×body640valid
7.3s69884×body80nan
5.9s12089×body320valid
4.8s3076×body1280nan
2.8s2577×body640nan
2.6s10086×body160valid
1.5s49536×pre80true
1.2s1284×body320nan
861.0ms1455×body2560valid
390.0ms585×body5120valid
285.0ms617×body160nan

series1.6m (5.7%)

Calls

510 calls:

4.5s
(- (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 (pow (fabs x) 2))) 3))
2.1s
(* (+ 1.0 (/ (* (/ 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 (pow (fabs x) 2)))) (/ (* (/ 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 (pow (fabs x) 2))))
2.1s
(* 0.16666666666666666 (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5))
1.9s
(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
1.7s
(* (* 0.16666666666666666 (pow (* (pow -1 1.0) (pow -2.0 1.0)) 0.5)) (pow (pow (- (log u1)) 1.0) 0.5))

regimes10.8s (0.6%)

Accuracy

Total 100.0b remaining (40.2%)

Threshold costs 5.3b (2.1%)

13.9b53.3%math.sqrt on complex, imaginary part, im greater than 0 branch
10.5b57.3%math.log10 on complex, real part
10.2b58.2%math.log/1 on complex, real part
10.1b58.8%math.log/2 on complex, real part
9.9b58.2%math.abs on complex

localize5.5s (0.3%)

bsearch2.5s (0.1%)

end1.0ms (0.0%)