Details

rewrite9.7m (37.5%)

Algorithm
163×rewrite-expression-head
Calls

512 calls:

4.0m
(* (/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z))))) (* (/ PI (sin (* PI z))) (+ (/ -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))))))))
1.2m
(* (/ (* (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)))))))
47.8s
(* (* (/ (* (pow (+ z 6.5) (- z 0.5)) (sqrt 2.0)) (exp (+ z 6.5))) (sqrt PI)) (+ (+ (/ -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)))))))
42.9s
(* (/ (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)))))))
35.6s
(* (* (* (/ (* (pow (+ z 6.5) (- z 0.5)) (sqrt 2.0)) (exp (+ z 6.5))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (+ (+ (/ -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
9447×times-frac
9273×*-un-lft-identity
7136×add-sqr-sqrt
5396×add-cube-cbrt
4910×frac-add
2907×sqrt-prod
2736×add-exp-log
2285×add-cbrt-cube
2037×flip-+ flip3-+
2020×distribute-lft-out
1801×associate-*l*
1795×pow1
1522×associate-*r/
1494×associate-*r*
1317×frac-times
1074×prod-exp
797×cbrt-unprod
742×add-log-exp
699×associate-/r/
672×associate-/l*
632×associate-*l/
531×div-exp
521×unpow-prod-down
515×flip3-- flip--
454×pow-prod-down
450×difference-of-squares
425×cbrt-undiv
408×associate-/r*
404×div-inv
377×sqrt-div
327×unswap-sqr
312×sqrt-pow1
289×cbrt-prod
287×distribute-lft-out--
233×swap-sqr
224×log-pow
214×frac-sub
184×associate-/l/
183×cbrt-div
178×pow1/2
169×cube-prod
164×*-commutative
155×pow-exp
144×sqr-pow
125×distribute-rgt-in distribute-lft-in
118×pow-prod-up
107×pow1/3
98×log-prod
93×pow-to-exp
88×pow-unpow
87×exp-prod
84×pow-sqr
82×rem-sqrt-square
81×frac-2neg clear-num
78×sum-log
74×sub-neg
65×exp-sum
48×diff-log
45×pow-plus +-commutative
39×pow-pow pow2
30×1-exp rec-exp
25×associate--l+
24×unpow3 cube-mult
21×div-sub distribute-rgt-neg-in
20×cube-div unpow-prod-up
18×rem-cube-cbrt
15×exp-diff associate-+l+ associate--r+
13×associate-+l-
10×log-div
unpow2
un-div-inv associate-+r- associate-+r+
rem-exp-log sin-sum
cos-sum sum-cubes
sqrt-unprod sub-div pow-sub rem-square-sqrt neg-sub0 sqrt-undiv
distribute-lft-neg-in rem-log-exp
sqrt-pow2 inv-pow exp-neg distribute-rgt-out-- unsub-neg pow-flip associate--r- rem-cbrt-cube
lft-mult-inverse neg-mul-1 cube-unmult associate--l-

simplify7.9m (30.8%)

sample3.5m (13.8%)

Algorithm
100×intervals
Results
1.0m15801×body10240exit
48.2s441895×body80valid
32.7s30693×body1280valid
17.1s23350×body640valid
7.8s68545×body80nan
5.4s3035×body1280nan
5.2s12132×body320valid
3.0s10283×body160valid
2.8s2596×body640nan
1.8s49536×pre80true
885.0ms1451×body2560valid
860.0ms1262×body320nan
856.0ms578×body5120valid
305.0ms655×body160nan

prune2.2m (8.6%)

series2.1m (8.0%)

Calls

512 calls:

20.8s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (+ (pow 0.254829592 3) (pow (* (/ 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))))))) 3)) (+ (* 0.254829592 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))))))) (- (* (/ 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))))))) 0.254829592))))) (exp (- (* (fabs x) (fabs x))))))
3.7s
(* (/ (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (sqrt (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
3.2s
(* (/ (/ (* 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))))
3.1s
(/ (+ (pow 0.254829592 3) (pow (* (/ 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))))))) 3)) (+ (* 0.254829592 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))))))) (- (* (/ 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))))))) 0.254829592))))
1.8s
(- (pow (* d1 (+ d4 (- d2 d3))) 3) (pow d1 6))

regimes11.7s (0.8%)

Accuracy

Total 95.6b remaining (34%)

Threshold costs 4.1b (1.5%)

17.2b44.9%math.log/2 on complex, real part
10.3b58%math.log10 on complex, real part
10.2b58.4%math.log/1 on complex, real part
10.1b57.5%math.abs on complex
9.2b56.8%math.sqrt on complex, real part

localize5.3s (0.3%)

bsearch2.7s (0.2%)

end1.0ms (0.0%)