Details

prune7.3m (32.3%)

rewrite7.0m (30.8%)

Algorithm
158×rewrite-expression-head
Calls

475 calls:

1.5m
(+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -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))))))
1.5m
(+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -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))))))
46.1s
(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) z) (sqrt (* PI 2.0))) (* (exp (+ (+ (- z 1.0) 7.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 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)))))))
45.9s
(* (exp (log (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) z) (sqrt (* PI 2.0))) (* (exp (+ (+ (- z 1.0) 7.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) 1.0))))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) 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))))))))
43.0s
(* (/ (* (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)))))))
Rules
104496×frac-add
97819×frac-times
57937×times-frac
38706×flip-+ flip3-+
34415×*-un-lft-identity
30636×flip-- flip3--
28403×associate-*r/
28109×frac-sub
24661×add-sqr-sqrt
22821×associate-*l/
22590×add-cube-cbrt
12460×sqrt-prod
5789×distribute-lft-out
3000×associate-/r/
2477×add-exp-log
1692×add-cbrt-cube
1665×div-inv
1634×associate-*l*
1436×associate-*r*
1423×pow1
1376×sqrt-div
950×prod-exp
885×add-log-exp
830×unpow-prod-down
705×associate-/l*
614×difference-of-squares
584×div-exp
553×associate-/r*
477×cbrt-prod
463×cbrt-unprod
336×distribute-lft-out--
320×cbrt-undiv
294×pow-prod-down
290×unswap-sqr
261×cube-prod
239×log-pow
225×sqr-pow
219×pow-exp
218×sum-log
193×cbrt-div
175×pow-to-exp
146×*-commutative
144×sqrt-pow1
141×log-prod
134×swap-sqr
130×associate-/l/
118×pow1/2
117×exp-diff
99×distribute-rgt-in distribute-lft-in
96×log-div
89×clear-num frac-2neg
86×pow1/3
79×pow-unpow
71×exp-prod
68×sub-neg
65×rem-sqrt-square
63×pow-prod-up
61×+-commutative
59×exp-sum
46×diff-log
43×pow-sqr
41×1-exp rec-exp
34×pow-plus
33×associate-+l-
28×pow-pow
22×pow2
20×unpow3 cube-mult
19×div-sub
17×pow-flip associate-+r+
16×associate--l+
11×rem-log-exp
10×rem-cube-cbrt pow-sub
cube-div inv-pow unpow-prod-up associate--r+
rem-exp-log
pow-div associate-+l+
difference-cubes
un-div-inv distribute-neg-frac
sqrt-undiv distribute-lft-neg-in pow3 sin-sum sum-cubes distribute-rgt-neg-in
sqrt-unprod distribute-neg-in distribute-rgt-out-- rem-square-sqrt associate--r- rem-cbrt-cube
cos-sum e-exp-1 remove-double-div neg-mul-1 distribute-rgt-neg-out exp-to-pow associate--l- unpow2

simplify5.8m (25.9%)

series1.2m (5.1%)

Calls

475 calls:

2.5s
(* (sqrt (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (* (sqrt (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
2.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
1.9s
(- 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 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (* (- 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))))))
1.2s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (sqrt (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))) (* (sqrt (/ 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))))))
1.1s
(* (sqrt (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))

sample1.2m (5.1%)

Algorithm
99×intervals
Results
18.4s468872×body80valid
13.7s30619×body1280valid
6.3s11736×body10240exit
6.0s22638×body640valid
2.5s70940×body80nan
2.1s11975×body320valid
1.1s10186×body160valid
980.0ms1587×body1280nan
614.0ms1301×body640nan
604.0ms49536×pre80true
347.0ms1509×body2560valid
231.0ms667×body320nan
136.0ms576×body5120valid
78.0ms335×body160nan

regimes6.0s (0.4%)

Accuracy

Total 99.5b remaining (35.6%)

Threshold costs 3.9b (1.4%)

16.8b49.8%math.sqrt on complex, imaginary part, im greater than 0 branch
10.5b58.2%math.log/2 on complex, real part
10.2b57.9%math.log10 on complex, real part
10.1b58.4%math.log/1 on complex, real part
9.9b57.8%math.abs on complex

localize2.8s (0.2%)

bsearch1.6s (0.1%)

end1.0ms (0.0%)