Details

rewrite9.9m (34.5%)

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)))))
55.4s
(* (/ (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)))))))
53.6s
(* (/ (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
100303×times-frac
53652×*-un-lft-identity
40507×add-sqr-sqrt
38400×add-cube-cbrt
8506×frac-add
7959×add-exp-log
7578×distribute-lft-out
5599×div-exp
5423×flip-+ flip3-+
4808×associate-/r/
4216×sqrt-prod
4210×div-inv
3340×associate-*r/
2635×frac-times
2566×add-cbrt-cube
2337×associate-*r*
2139×pow1
1843×associate-/l*
1771×prod-exp
1569×1-exp
1322×associate-*l*
947×associate-/r*
848×unpow-prod-down
845×add-log-exp
837×rec-exp
801×difference-of-squares
786×cbrt-unprod
673×associate-*l/
649×cbrt-undiv
648×pow-prod-down
578×distribute-lft-out--
490×log-pow
414×cbrt-prod
364×flip3-- flip--
341×associate-+l-
339×unswap-sqr
332×cube-prod
331×pow-sub
326×frac-sub
321×sqrt-div
312×sqrt-pow1
253×cbrt-div
230×exp-sum
199×pow1/2
171×sqr-pow
163×sum-log
161×*-commutative
146×sub-neg
142×pow1/3
140×associate-/l/
139×pow-exp
132×pow-prod-up
120×distribute-rgt-in distribute-lft-in
110×swap-sqr
102×frac-2neg clear-num
95×pow-to-exp
87×log-prod
78×pow-unpow
72×rem-sqrt-square
68×pow-plus
64×pow-sqr
56×unpow-prod-up
54×+-commutative
41×diff-log
39×unpow3 cube-mult
38×pow-pow
36×rem-cube-cbrt exp-prod
32×pow2
23×exp-diff
21×cube-div div-sub
19×distribute-rgt-neg-in
17×associate--l+
14×associate-+r+
13×inv-pow pow-flip
12×sub-div
10×un-div-inv
rem-exp-log pow3 associate-+r-
associate-+l+ exp-to-pow associate--r+
difference-of-sqr--1 sqrt-unprod distribute-neg-in log-div
rem-cbrt-cube
rem-square-sqrt neg-sub0 rem-log-exp
sin-sum unpow2
pow-div unsub-neg
cos-sum sqrt-undiv difference-cubes sqrt-pow2 distribute-rgt-out-- associate--r- associate--l-

simplify8.1m (28.1%)

prune4.7m (16.4%)

sample3.9m (13.5%)

Algorithm
100×intervals
Results
1.1m496506×body80valid
1.0m15777×body10240exit
34.8s30244×body1280valid
16.1s23335×body640valid
8.1s69884×body80nan
5.5s12089×body320valid
5.3s3076×body1280nan
3.2s10086×body160valid
2.8s2577×body640nan
1.5s49536×pre80true
1.0s1284×body320nan
910.0ms1423×body2560valid
836.0ms617×body5120valid
426.0ms617×body160nan

series1.9m (6.5%)

Calls

510 calls:

4.8s
(- (pow 1.0 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 (pow (fabs x) 2))) 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 (pow (fabs x) 2))) 3))))
4.8s
(- (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))
4.6s
(- (pow 1.0 3) (* (sqrt (log (exp (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)))) (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 (pow (fabs x) 2))) 3))))
4.3s
(* (+ (sqrt (* d1 (+ d4 (- d2 d3)))) d1) (- (sqrt (* d1 (+ d4 (- d2 d3)))) d1))
2.3s
(* (/ (* (/ 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 (+ 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)))))

regimes10.6s (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
10.6b57.2%math.log10 on complex, real part
10.2b58.2%math.log/1 on complex, real part
10.2b58.8%math.log/2 on complex, real part
9.9b58.2%math.abs on complex

localize4.7s (0.3%)

bsearch2.5s (0.1%)

end1.0ms (0.0%)