Details

simplify7.7m (35.6%)

rewrite7.0m (32.4%)

Algorithm
157×rewrite-expression-head
Calls

484 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)))))
59.4s
(+ (+ (+ (+ (/ -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)))))
54.2s
(* (exp (- (- 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)))))))
41.6s
(+ (+ (+ (+ (/ -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)))))
Rules
11202×times-frac
9173×*-un-lft-identity
7410×add-sqr-sqrt
6011×add-cube-cbrt
3219×sqrt-prod
3190×frac-add
2225×add-exp-log
1803×add-cbrt-cube
1647×flip-+ flip3-+
1537×distribute-lft-out
1457×pow1
1122×associate-*l*
991×associate-*r/
949×associate-*r*
937×add-log-exp
755×frac-times
745×associate-/r*
739×prod-exp
714×associate-/r/
692×associate-/l*
586×cbrt-unprod
480×div-exp
456×unpow-prod-down
448×cbrt-div
447×cbrt-prod
407×div-inv
356×cbrt-undiv
312×difference-of-squares
301×pow-prod-down
277×unswap-sqr
274×associate-*l/ sum-log
264×distribute-lft-out--
262×exp-diff
254×sqrt-div
208×sqrt-pow1
201×swap-sqr
185×log-pow
158×associate-/l/
155×flip3-- flip--
145×exp-sum
136×pow1/2
133×log-prod
131×*-commutative
130×sqr-pow
126×pow1/3
95×cube-prod
92×clear-num frac-2neg
90×pow-prod-up
88×sub-neg
81×distribute-rgt-in distribute-lft-in
76×unpow-prod-up pow-exp
68×rem-sqrt-square
62×pow-unpow
60×pow-sqr
59×pow-to-exp
57×+-commutative
38×1-exp rec-exp
35×pow-plus
34×pow-pow
33×diff-log
30×pow2 exp-prod
25×unpow3 cube-mult
22×log-div
21×associate--l+
20×cube-div
19×associate-+r+ associate-+l-
17×div-sub
16×associate-+l+
13×distribute-rgt-neg-in
10×pow-sub rem-log-exp
rem-exp-log inv-pow sin-sum pow-flip associate-+r-
rem-cube-cbrt
rem-cbrt-cube
distribute-lft-neg-out unsub-neg neg-sub0 associate--r+ unpow2
un-div-inv sqrt-unprod rem-square-sqrt
associate--r- frac-sub exp-to-pow
cos-sum sqrt-pow2 distribute-rgt-out-- distribute-rgt-out sum-cubes

sample3.5m (16.0%)

Algorithm
99×intervals
Results
57.6s15544×body10240exit
50.0s437767×body80valid
30.1s30263×body1280valid
15.1s23358×body640valid
8.1s69959×body80nan
5.7s12027×body320valid
5.2s3043×body1280nan
3.9s2442×body640nan
3.3s9993×body160valid
1.6s49536×pre80true
1.4s1468×body2560valid
846.0ms1320×body320nan
580.0ms630×body160nan
442.0ms569×body5120valid

prune1.8m (8.3%)

series1.4m (6.4%)

Calls

484 calls:

1.5s
(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
1.5s
(- 1.0 (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ (sqrt 1.0) (* (cbrt (+ 1.0 (* 0.3275911 (fabs x)))) (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))) (* (/ (sqrt 1.0) (cbrt (+ 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))))) (+ 1.0 (* 0.3275911 (fabs x)))))
1.2s
(- 1.0 (/ (* 1.0 (/ (+ (+ 0.254829592 (* -0.284496736 (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ (/ 1.0 (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))) (exp (* (fabs x) (fabs x))))) (+ 1.0 (* 0.3275911 (fabs x)))))
1.2s
(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))
1.1s
(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

regimes9.4s (0.7%)

Accuracy

Total 95.6b remaining (34%)

Threshold costs 4.6b (1.6%)

16.4b46.5%math.log/2 on complex, real part
10.2b57.8%math.log10 on complex, real part
10.0b58.5%math.log/1 on complex, real part
9.6b58.6%math.abs on complex
9.4b55%math.sqrt on complex, imaginary part, im greater than 0 branch

localize5.2s (0.4%)

bsearch3.1s (0.2%)

end1.0ms (0.0%)