Details

prune8.8m (33.5%)

simplify8.6m (33.0%)

sample3.8m (14.6%)

Algorithm
100×intervals
Results
1.1m496506×body80valid
58.7s15777×body10240exit
32.0s30244×body1280valid
15.4s23335×body640valid
7.8s69884×body80nan
6.4s12089×body320valid
5.6s3076×body1280nan
3.8s2577×body640nan
2.6s10086×body160valid
1.5s49536×pre80true
1.2s1284×body320nan
871.0ms1423×body2560valid
372.0ms617×body160nan
349.0ms617×body5120valid

rewrite2.8m (10.5%)

Algorithm
156×rewrite-expression-head
Calls

476 calls:

1.5m
(* (/ (* (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))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099))))))
23.6s
(+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z))))))))
5.4s
(/ (/ (fma -1259.1392167224028 (* (* (- 3.0 z) (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (- 4.0 z)))) (* (* (- 5.0 z) (- 8.0 z)) (- (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z))))) (* (+ (- z) 2.0) (fma (fma (- (* (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (* (/ -176.6150291621406 (- 4.0 z)) (/ -176.6150291621406 (- 4.0 z)))) (- 3.0 z) (* (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (- 4.0 z))) 771.3234287776531)) (* (* (- 5.0 z) (- 8.0 z)) (- (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z)))) (* (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (- 4.0 z))) (* (- 3.0 z) (fma 12.507343278686905 (* (- (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z))) (- 8.0 z)) (* (- 5.0 z) (fma 1.5056327351493116e-07 (- (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z))) (* (- (* (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0))) (* (/ -0.13857109526572012 (- 6.0 z)) (/ -0.13857109526572012 (- 6.0 z)))) (- 8.0 z)))))))))) (* (+ (- z) 2.0) (* (* (- 3.0 z) (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (- 4.0 z)))) (* (* (- 5.0 z) (- 8.0 z)) (- (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z))))))) (exp (+ 0.5 (+ (- z) 7.0))))
3.2s
(/ (* (- (- z) 2.0) (* (* (+ 3.0 z) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (- 4.0 z)))) (* (* (+ (* 5.0 5.0) (+ (* z z) (* 5.0 z))) (+ (* 8.0 8.0) (+ (* z z) (* 8.0 z)))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z)))))) (exp (+ (- z) 7.0)))
3.1s
(* (* (sqrt (/ 1 PI)) (exp (pow (fabs x) 2))) (+ (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (/ 1.875 (pow (fabs x) 7))) (/ 0.5 (pow (fabs x) 3))))
Rules
31517×frac-times
17092×times-frac
13625×*-un-lft-identity
12376×flip3-- flip--
9899×add-sqr-sqrt
9694×associate-*r/
8294×associate-/r/
7492×add-cube-cbrt
7463×flip-+ flip3-+
6018×associate-*l/
5266×frac-sub
2644×distribute-lft-out
2311×sqrt-prod
2303×associate-/l*
2249×add-exp-log
1935×frac-add
1819×exp-sum
1728×add-cbrt-cube
1703×associate-/l/
1378×pow1
1093×prod-diff
1049×associate-*l*
1007×associate-*r*
727×add-log-exp
697×prod-exp
691×distribute-lft-out--
689×difference-of-squares
579×cbrt-prod
571×associate-/r*
547×div-exp
482×log1p-expm1-u
477×cbrt-unprod
476×expm1-log1p-u
442×unpow-prod-down
394×div-inv
361×unswap-sqr
353×cbrt-undiv
327×swap-sqr
321×pow-prod-down
257×cube-prod
202×fma-def
175×distribute-rgt-in distribute-lft-in
171×sqrt-pow1
168×sqr-pow
158×log-pow
151×fma-neg
129×*-commutative
124×sum-log
118×cbrt-div
103×frac-2neg clear-num distribute-rgt-neg-in
100×pow1/2
93×pow1/3
90×pow-exp
89×pow-unpow
86×distribute-lft-neg-in
75×sqrt-div
74×1-exp
73×unpow3 cube-mult
72×rec-exp
62×pow-prod-up
60×sub-neg
55×fma-udef
53×pow-to-exp associate--l+
46×pow-sqr
45×log-prod
44×diff-log associate-+l+
40×rem-sqrt-square
36×pow-pow
35×associate-+l-
31×exp-prod
27×pow-plus +-commutative
25×exp-diff
23×pow2
22×neg-mul-1
21×rem-cube-cbrt
16×div-sub
14×hypot-udef
13×cube-div
12×un-div-inv pow-flip neg-sub0
10×inv-pow
exp-neg expm1-udef
sqrt-unprod expm1-log1p associate--r+
log1p-udef rem-log-exp associate--l-
associate-+r+
log1p-expm1 distribute-neg-in pow-sub rem-square-sqrt
unpow-prod-up hypot-def rem-cbrt-cube
distribute-rgt-neg-out
rem-exp-log difference-cubes sqrt-pow2 sum-cubes associate-+r- pow3 sin-sum sub-div distribute-frac-neg cos-sum associate--r- unpow2

series2.0m (7.5%)

Calls

476 calls:

11.3s
(+ (pow (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 3) (pow 1.0 3))
4.4s
(* (+ (sqrt (* d1 (- (+ d4 d2) d3))) d1) (- (sqrt (* d1 (- (+ d4 d2) d3))) d1))
1.7s
(- (pow 1.0 3) (log1p (expm1 (log (exp (pow (* (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (/ (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (exp (pow (fabs x) 2)))) 3))))))
1.7s
(* (cbrt (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))) (cbrt (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))))
1.6s
(* (sqrt (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (sqrt (/ (pow (* -2.0 (log u1)) 0.5) 6.0)))

regimes7.8s (0.5%)

Accuracy

Total 24.2b remaining (18.4%)

Threshold costs 8.8b (6.7%)

9.1b17.6%_divideComplex, real part
2.9b77.4%Octave 3.8, jcobi/1
2.4b31.3%Octave 3.8, jcobi/4
1.1b0%Jmat.Real.lambertw, newton loop step
0.9b60.8%Octave 3.8, jcobi/3

localize6.0s (0.4%)

bsearch915.0ms (0.1%)

end1.0ms (0.0%)