Details

simplify10.0m (40.8%)

prune5.2m (21.4%)

sample3.9m (16.0%)

Algorithm
100×intervals
Results
1.4m16218×body10240exit
51.1s452669×body80valid
30.2s30691×body1280valid
16.7s23544×body640valid
7.5s69725×body80nan
6.9s3170×body1280nan
6.4s12027×body320valid
3.7s2580×body640nan
2.6s10167×body160valid
2.3s1339×body320nan
2.1s49536×pre80true
971.0ms1473×body2560valid
588.0ms654×body160nan
304.0ms636×body5120valid

rewrite3.0m (12.4%)

Algorithm
161×rewrite-expression-head
Calls

485 calls:

1.2m
(* (+ (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0)))) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -176.6150291621406 (+ 4.0 (- z 1.0)))) (+ (/ 771.3234287776531 (+ 3.0 (- z 1.0))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099)))))) (* (/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0))))) (sqrt (* 2.0 PI))))
1.1m
(* (+ (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0)))) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -176.6150291621406 (+ 4.0 (- z 1.0)))) (+ (/ 771.3234287776531 (+ 3.0 (- z 1.0))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099)))))) (/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0))))))
9.2s
(+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- 0 z))) (/ 12.507343278686905 (+ (- 0 z) 5.0))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0)))))
3.1s
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
1.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
Rules
29328×times-frac
24705×frac-times
18242×*-un-lft-identity
16666×add-sqr-sqrt
15963×associate-*r/
11965×add-cube-cbrt
9826×associate-*l/
8131×flip-+ flip3-+
7864×exp-neg
7708×frac-add
6744×exp-diff
6740×neg-sub0
4548×sqrt-prod
3623×pow1
3042×add-exp-log
2553×add-cbrt-cube
2231×distribute-lft-out
1902×associate-/r/
1894×difference-of-squares
1569×associate-*r*
1315×div-inv
1202×prod-exp
1141×associate-*l*
1135×un-div-inv
1047×distribute-lft-out--
1024×pow-prod-up
955×cbrt-unprod
843×pow-prod-down
800×associate-/l*
776×cbrt-prod
719×add-log-exp
717×div-exp
653×prod-diff
645×associate-/r*
547×pow-plus
511×cbrt-undiv
487×log1p-expm1-u
486×expm1-log1p-u
323×unswap-sqr
308×pow-sqr
209×unpow-prod-down
198×pow2
192×swap-sqr
190×fma-def
181×sqrt-pow1
163×*-commutative
157×exp-sum
150×log-pow
121×sum-log sqrt-div
120×pow-exp
114×flip3-- flip--
113×distribute-rgt-in distribute-lft-in
112×fma-neg
96×pow1/3
92×frac-2neg clear-num
87×cbrt-div
79×fma-udef
72×pow1/2
70×sqr-pow associate-/l/
69×1-exp
68×log-prod
67×rec-exp
57×pow-to-exp
54×cube-div
51×cube-prod
43×cube-unmult
41×sub-neg
40×exp-prod
38×pow3
37×+-commutative
31×pow-unpow rem-sqrt-square
26×unpow3 cube-mult
25×diff-log
23×distribute-rgt-out
20×associate-+l+ frac-sub
19×distribute-rgt1-in pow-pow
17×div-sub
16×associate-+r+
15×unpow-prod-up
12×rem-cube-cbrt
11×hypot-def
10×pow-flip
distribute-lft-neg-in associate-+r- distribute-rgt-neg-in
inv-pow
sin-sum
associate--r+ associate--l+ rem-exp-log cos-sum
expm1-log1p expm1-udef neg-log
pow-sub associate-+l-
sqrt-undiv log1p-expm1 log1p-udef sqrt-unprod neg-mul-1 hypot-udef rem-square-sqrt count-2 rem-log-exp
distribute-rgt-neg-out difference-cubes distribute-neg-in rem-cbrt-cube associate--r- log-div

series1.9m (7.8%)

Calls

485 calls:

4.6s
(- (pow 1.0 3) (pow (* (* (/ 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 (* (cbrt (+ 1.0 (* 0.3275911 (fabs x)))) (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))) (cbrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3))
3.9s
(+ (* (* (* (/ 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 (* (cbrt (+ 1.0 (* 0.3275911 (fabs x)))) (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))) (cbrt (+ 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 (* (cbrt (+ 1.0 (* 0.3275911 (fabs x)))) (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))) (cbrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))) (* 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 (* (cbrt (+ 1.0 (* 0.3275911 (fabs x)))) (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))) (cbrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))
3.7s
(* (/ (/ (* 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))))
3.6s
(/ (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
3.5s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))

regimes13.1s (0.9%)

Accuracy

Total 25.4b remaining (16.9%)

Threshold costs 8.3b (5.5%)

7.8b32.5%_divideComplex, real part
3.0b-1.8%_divideComplex, imaginary part
2.8b76.8%Octave 3.8, jcobi/1
2.3b37.2%Octave 3.8, jcobi/4
1.2b68.7%Octave 3.8, jcobi/3

localize11.2s (0.8%)

bsearch969.0ms (0.1%)

end2.0ms (0.0%)