Details

rewrite11.2m (37.3%)

Algorithm
149×rewrite-expression-head
Calls

444 calls:

28.8s
(+ (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 12.507343278686905 (+ (- z) 5.0))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (+ (- z) 4.0)) (/ -1259.1392167224028 (+ (- z) 2.0)))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
8.3s
(+ (+ (/ 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)))))
4.1s
(+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 12.507343278686905 (+ (- z) 5.0))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (+ (- z) 4.0)) (/ -1259.1392167224028 (+ (- z) 2.0))))))
2.7s
(+ (+ 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))))
2.0s
(+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- 0 z))) (/ 12.507343278686905 (+ (- 0 z) 5.0))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (fma (/ 1 (* (cbrt (+ 3.0 (- 0 z))) (cbrt (+ 3.0 (- 0 z))))) (/ 771.3234287776531 (cbrt (+ 3.0 (- 0 z)))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0)))))
Rules
23639×frac-times
17217×times-frac
15642×associate-*r/
13977×*-un-lft-identity
10187×add-sqr-sqrt
9263×associate-*l/
8548×add-cube-cbrt
7581×exp-neg
7260×frac-add
7199×flip-+ flip3-+
6501×exp-diff
6498×neg-sub0
2947×pow1
2859×sqrt-prod
2613×distribute-lft-out
2180×add-exp-log
1883×add-cbrt-cube
1621×associate-*l*
1087×un-div-inv
1001×associate-*r*
981×add-log-exp
931×prod-diff
821×associate-/l*
795×pow-prod-up
763×prod-exp
760×cbrt-prod
627×pow-prod-down
619×cbrt-unprod
611×div-inv
576×associate-/r*
488×associate-/r/
478×difference-of-squares
449×div-exp
443×expm1-log1p-u
442×log1p-expm1-u
387×distribute-lft-out--
368×pow-plus
363×cbrt-undiv
355×sum-log
265×unswap-sqr
256×distribute-rgt-in distribute-lft-in
247×pow-sqr
210×log-pow
183×swap-sqr
166×log-prod
162×pow2
152×fma-def
143×flip3-- *-commutative flip--
133×sqrt-div
130×cbrt-div
126×sqrt-pow1
120×exp-sum
103×fma-neg
90×frac-2neg clear-num
83×associate-/l/
76×fma-udef
72×pow1/3
67×associate--l+
63×sub-neg
56×pow1/2
55×unpow-prod-down
45×1-exp cube-unmult rec-exp
42×cube-prod sqr-pow
39×diff-log
33×distribute-rgt-out
29×+-commutative
26×pow-exp distribute-rgt-neg-in
22×frac-sub unpow3 cube-mult
21×div-sub exp-prod
20×distribute-rgt1-in
18×cube-div
17×associate-+l+ rem-sqrt-square
16×pow3
15×associate-+r+
14×pow-to-exp
12×pow-unpow
11×rem-log-exp
9×pow-pow hypot-def
8×sin-sum
7×log-div
6×distribute-lft1-in difference-cubes cos-sum count-2
5×pow-flip pow-div associate--r+ inv-pow
4×rem-cube-cbrt
3×log1p-expm1 sqrt-unprod associate-+l- log1p-udef
2×expm1-log1p expm1-udef associate--l- exp-to-pow hypot-udef rem-square-sqrt associate--r-
1×associate-+r- distribute-rgt-out-- rem-exp-log rem-cbrt-cube

simplify9.1m (30.3%)

prune4.4m (14.6%)

sample3.3m (11.1%)

Algorithm
98×intervals
Results
1.2m12154×body10240exit
45.2s437147×body80valid
26.5s27121×body1280valid
12.9s21329×body640valid
7.4s67962×body80nan
4.5s10658×body320valid
4.4s1648×body1280nan
2.2s1340×body640nan
2.1s9643×body160valid
1.6s49536×pre80true
1.3s1496×body2560valid
1.1s669×body320nan
370.0ms625×body5120valid
265.0ms339×body160nan

series1.7m (5.5%)

Calls

441 calls:

5.1s
(- (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 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3))
4.1s
(+ (* (* (* (/ 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))))) (* (* (/ 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)))))) (* 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)))))))
3.5s
(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) 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))))
3.4s
(* (/ (/ (* 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))))
1.7s
(log1p (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0))

regimes11.9s (0.7%)

Accuracy

Total 33.2b remaining (25.9%)

Threshold costs 5.0b (3.9%)

10.8b16.5%Octave 3.8, jcobi/4
8.5b28.8%_divideComplex, real part
3.2b0%_divideComplex, imaginary part
2.9b77.5%Octave 3.8, jcobi/1
1.7b0%Jmat.Real.lambertw, newton loop step

localize7.6s (0.4%)

bsearch1.0s (0.1%)

end1.0ms (0.0%)