Details

rewrite8.0m (34.0%)

Algorithm
157×rewrite-expression-head
Calls

485 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)))))
58.6s
(* (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)))))))
44.3s
(+ (+ (+ (+ (/ -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
37416×times-frac
22446×*-un-lft-identity
17360×add-sqr-sqrt
15763×add-cube-cbrt
7326×sqrt-prod
4983×frac-add
3287×distribute-lft-out
2467×flip-+ flip3-+
2426×add-exp-log
1909×add-cbrt-cube
1700×cbrt-prod
1630×pow1
1467×div-inv
1431×associate-/r/
1373×associate-*r/
1286×associate-/l*
1166×associate-*l*
1164×frac-times
1049×associate-*r*
914×unpow-prod-down
879×add-log-exp
783×prod-exp
776×associate-/r*
628×div-exp
611×cbrt-unprod
506×exp-diff
439×cbrt-div log-pow
422×cube-prod
408×cbrt-undiv
358×difference-of-squares
306×distribute-lft-out--
303×unswap-sqr
299×associate-*l/
297×pow-prod-down
283×swap-sqr
273×sqrt-div
270×sqrt-pow1
226×sum-log
208×pow1/2
197×exp-sum
191×sqr-pow
161×flip3-- flip--
159×associate-/l/
131×*-commutative
127×log-prod
120×pow1/3
119×unpow-prod-up
112×sub-neg
91×clear-num frac-2neg
90×pow-exp
87×pow-prod-up
82×distribute-rgt-in distribute-lft-in
77×pow-unpow
68×pow-to-exp
67×1-exp
62×rem-sqrt-square
61×pow-sqr
58×+-commutative
49×rec-exp
39×pow-pow
35×pow-plus
33×diff-log
32×cube-div
30×unpow3 pow2 cube-mult exp-prod
23×associate--l+
22×associate-+l-
20×log-div
19×div-sub
17×rem-cube-cbrt
15×associate-+l+ associate-+r+
9×rem-exp-log sin-sum pow-sub
8×distribute-rgt-neg-in rem-log-exp
7×inv-pow pow-flip rem-cbrt-cube
5×associate-+r-
4×distribute-lft-neg-out sqrt-unprod rem-square-sqrt associate--r+ unpow2
3×un-div-inv unsub-neg
2×neg-sub0 associate--r- frac-sub exp-to-pow
1×cos-sum difference-cubes sqrt-pow2 distribute-rgt-out-- unpow1/2 distribute-rgt-out sum-cubes

simplify7.4m (31.4%)

sample3.5m (14.8%)

Algorithm
99×intervals
Results
58.6s15544×body10240exit
50.0s437767×body80valid
30.2s30263×body1280valid
16.8s23358×body640valid
6.7s69959×body80nan
5.4s3043×body1280nan
5.3s12027×body320valid
3.4s9993×body160valid
2.9s2442×body640nan
1.9s49536×pre80true
1.1s1468×body2560valid
957.0ms1320×body320nan
581.0ms630×body160nan
449.0ms569×body5120valid

prune2.8m (12.0%)

series1.5m (6.4%)

Calls

485 calls:

4.6s
(- (pow 1.0 3) (pow (/ (/ (+ 0.254829592 (/ (* 1.0 (+ -0.284496736 (/ 1.0 (/ (+ (* 0.3275911 (fabs x)) 1.0) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (+ (* 0.3275911 (fabs x)) 1.0))) (/ (exp (pow (fabs x) 2)) 1.0)) (+ (* 0.3275911 (fabs x)) 1.0)) 3))
2.1s
(* (* (+ 1.0 (/ (/ (+ 0.254829592 (/ (* 1.0 (+ -0.284496736 (/ 1.0 (/ (+ (* 0.3275911 (fabs x)) 1.0) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (+ (* 0.3275911 (fabs x)) 1.0))) (/ (exp (pow (fabs x) 2)) 1.0)) (+ (* 0.3275911 (fabs x)) 1.0))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))) (/ (+ 0.254829592 (/ (* 1.0 (+ -0.284496736 (/ 1.0 (/ (+ (* 0.3275911 (fabs x)) 1.0) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (+ (* 0.3275911 (fabs x)) 1.0))) (exp (pow (fabs x) 2))))
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)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))) (/ (/ 1.0 (* (cbrt (+ 1.0 (* 0.3275911 (fabs x)))) (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))) (cbrt (+ 1.0 (* 0.3275911 (fabs x))))))) (exp (* (fabs x) (fabs x))))) (+ 1.0 (* 0.3275911 (fabs x)))))
1.2s
(- 1.0 (/ (* 1.0 (/ (+ 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 (* (fabs x) (fabs x))))) (+ 1.0 (* 0.3275911 (fabs x)))))
1.2s
(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

regimes10.0s (0.7%)

Accuracy

Total 95.2b remaining (34.1%)

Threshold costs 5.0b (1.8%)

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
8.8b59.7%math.sqrt on complex, real part

localize5.1s (0.4%)

bsearch3.5s (0.2%)

end1.0ms (0.0%)