Details

rewrite9.3m (35.8%)

Algorithm
163×rewrite-expression-head
Calls

509 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)))))
1.0m
(+ (+ (+ (+ (/ -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)))))
49.5s
(* (/ (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))))))))
47.4s
(* (/ (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)))))))
Rules
19247×times-frac
15619×*-un-lft-identity
10331×add-sqr-sqrt
8929×add-cube-cbrt
8507×frac-add
3829×flip-+ flip3-+
3635×distribute-lft-out
3357×associate-*r/
2714×add-exp-log
2673×frac-times
2183×add-cbrt-cube
1897×pow1
1766×sqrt-prod
1338×associate-*l*
1273×associate-*r*
1048×associate-/r/
971×prod-exp
871×associate-/l*
851×add-log-exp
799×div-inv
754×associate-/r*
738×cbrt-unprod
688×unpow-prod-down
668×associate-*l/
654×div-exp
573×pow-prod-down
439×cbrt-prod
396×cbrt-undiv
341×associate-+l-
331×pow-sub
329×unswap-sqr
326×frac-sub
300×log-pow
295×difference-of-squares
276×sqrt-div
252×cbrt-div
251×flip3-- flip--
240×distribute-lft-out--
238×exp-sum
234×sqrt-pow1
181×cube-prod
166×sum-log
156×*-commutative
153×sqr-pow
147×sub-neg
144×pow1/2
138×associate-/l/
135×swap-sqr
118×distribute-rgt-in distribute-lft-in
105×log-prod
102×pow-exp
99×frac-2neg clear-num
95×pow1/3
72×pow-unpow
71×pow-to-exp
70×1-exp
67×rem-sqrt-square
64×rec-exp
62×pow-prod-up
57×+-commutative
56×unpow-prod-up
44×pow-sqr
42×exp-prod diff-log
36×pow-pow
33×unpow3 cube-mult
24×exp-diff rem-cube-cbrt pow-plus
20×pow2
19×distribute-rgt-neg-in
18×associate-+r+
17×associate--l+
16×cube-div div-sub
15×pow-flip
14×log-div
13×rem-log-exp
12×sub-div
11×un-div-inv
10×rem-exp-log inv-pow
associate-+r-
associate-+l+ associate--r+
exp-to-pow
distribute-neg-in difference-of-sqr--1
unpow2
sqrt-unprod rem-square-sqrt neg-sub0 rem-cbrt-cube
sin-sum
distribute-rgt-out-- unsub-neg
cos-sum sqrt-undiv difference-cubes sqrt-pow2 pow3 associate--r- associate--l-

simplify7.8m (30.2%)

sample3.8m (14.8%)

Algorithm
100×intervals
Results
1.1m496506×body80valid
1.0m15777×body10240exit
28.6s30244×body1280valid
15.7s23335×body640valid
8.4s69884×body80nan
5.3s3076×body1280nan
4.8s12089×body320valid
4.0s10086×body160valid
2.9s2577×body640nan
1.8s49536×pre80true
924.0ms1284×body320nan
737.0ms1423×body2560valid
553.0ms617×body5120valid
264.0ms617×body160nan

prune2.9m (11.0%)

series1.8m (6.9%)

Calls

509 calls:

4.7s
(- (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))))
4.6s
(- (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 (pow (fabs x) 2))) 3))
4.5s
(* (+ (sqrt (* d1 (+ d4 (- d2 d3)))) d1) (- (sqrt (* d1 (+ d4 (- d2 d3)))) d1))
2.1s
(* (/ (* (/ 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)))))
2.1s
(* (/ (* (/ 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)))))

regimes9.9s (0.6%)

Accuracy

Total 107.0b remaining (43%)

Threshold costs 5.1b (2%)

17.5b44.7%math.log/2 on complex, real part
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
9.9b58.2%math.abs on complex

localize5.3s (0.3%)

bsearch3.2s (0.2%)

end1.0ms (0.0%)