Details

simplify8.2m (33.5%)

rewrite6.8m (27.9%)

Algorithm
164×rewrite-expression-head
Calls

505 calls:

1.2m
(* (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))))
48.4s
(* (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (exp (+ (* (+ (- z 1.0) 0.5) (log (+ (+ (- z 1.0) 7.0) 0.5))) (log (sqrt (* PI 2.0))))))
46.5s
(/ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (/ (exp z) (exp (fma (+ (- z 1.0) 0.5) (log (+ (+ (- z 1.0) 7.0) 0.5)) (log (sqrt (* PI 2.0)))))))
44.8s
(* (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (/ (exp (- (- 1.0 7.0) 0.5)) (exp (- z (fma (+ (- z 1.0) 0.5) (log (+ (+ (- z 1.0) 7.0) 0.5)) (log (sqrt (* PI 2.0))))))))
44.2s
(* (/ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (/ (exp z) (exp (fma (+ (- z 1.0) 0.5) (log (+ (+ (- z 1.0) 7.0) 0.5)) (log (sqrt (* PI 2.0))))))) (exp (- (- 1.0 7.0) 0.5)))
Rules
23817×times-frac
20520×*-un-lft-identity
13450×add-sqr-sqrt
12122×add-cube-cbrt
5568×distribute-lft-out
5484×sqrt-prod
5051×add-exp-log
4499×pow1
4000×add-cbrt-cube
2980×frac-add
2941×prod-exp
2302×cbrt-unprod
2243×pow-prod-down
1893×prod-diff
1706×associate-*r*
1698×associate-*l*
1059×exp-sum
1046×flip-+ flip3-+
829×div-inv
822×add-log-exp
776×associate-*l/
725×div-exp
697×pow-prod-up
671×associate-/l*
626×sqrt-pow1
597×associate-/r*
507×log1p-expm1-u
506×expm1-log1p-u
454×cbrt-undiv
410×frac-times
363×associate-/l/
339×unswap-sqr
307×cbrt-prod
301×associate--l+
297×distribute-rgt-in distribute-lft-in
293×log-pow
272×difference-of-squares
270×associate-*r/
266×pow1/2
259×pow-plus
251×swap-sqr
247×distribute-lft-out--
233×associate-/r/ pow-sqr
227×pow1/3
221×log-prod
216×flip3-- flip--
212×fma-udef
175×fma-neg
171×cbrt-div
168×*-commutative
162×sub-neg
149×associate-+l-
148×sum-log
143×pow-sub
139×pow-exp
136×fma-def
109×sqrt-div
104×pow2
95×frac-2neg clear-num
94×exp-prod
73×pow-to-exp
66×1-exp
63×diff-log
60×distribute-rgt-out
58×rec-exp
40×associate-+l+
37×unpow-prod-down
36×associate-+r+ pow-flip
34×+-commutative
32×sqr-pow
26×rem-sqrt-square
24×cube-unmult
22×distribute-rgt1-in frac-sub
19×pow-unpow
18×sqrt-unprod
16×distribute-rgt-neg-in div-sub distribute-lft-neg-in
15×rem-log-exp
14×exp-diff
13×hypot-udef
12×associate--l-
10×inv-pow
count-2
distribute-lft1-in pow3
hypot-def log-div
pow-pow un-div-inv cos-sum
associate--r+ rem-square-sqrt
sin-sum neg-mul-1
expm1-log1p expm1-udef exp-to-pow
rem-exp-log associate--r-
unpow-prod-up associate-+r- log1p-expm1 log-rec distribute-rgt-out-- rem-cbrt-cube log1p-udef

sample4.0m (16.3%)

Algorithm
100×intervals
Results
1.4m16169×body10240exit
54.8s459773×body80valid
32.3s31044×body1280valid
15.2s23726×body640valid
6.7s69248×body80nan
6.0s3116×body1280nan
5.4s2701×body640nan
5.2s11802×body320valid
3.6s10206×body160valid
1.7s1222×body320nan
1.5s49536×pre80true
1.0s1531×body2560valid
734.0ms597×body5120valid
419.0ms698×body160nan

prune3.4m (13.9%)

series1.6m (6.7%)

Calls

505 calls:

7.5s
(- (* 1.0 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 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 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 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))
1.7s
(- 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 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))
1.5s
(* (sqrt (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
1.2s
(/ (- (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
1.1s
(- 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 (* 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))))))

regimes14.6s (1.0%)

Accuracy

Total 31.3b remaining (21.9%)

Threshold costs 5.7b (4%)

7.5b34.2%_divideComplex, real part
5.9b13.7%Octave 3.8, jcobi/2
3.4b0%_divideComplex, imaginary part
3.1b75.5%Octave 3.8, jcobi/1
2.6b29.4%Octave 3.8, jcobi/4

localize10.6s (0.7%)

bsearch966.0ms (0.1%)

end1.0ms (0.0%)