Details

series9.3m (29.8%)

Calls

485 calls:

7.0m
(- (pow 1.0 3) (pow (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (* (+ (fma (/ -1 (fma (fabs x) 0.3275911 1.0)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (+ (+ 0.254829592 (- (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) (+ (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3)) (/ 0.284496736 (fma (fabs x) 0.3275911 1.0))))) (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)))) (exp (- (pow (fabs x) 2))))) 3))
33.9s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (+ (+ (- (+ 0.254829592 (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2))) (/ 0.284496736 (fma (fabs x) 0.3275911 1.0))) (/ (- (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 2))) (fma (fabs x) 0.3275911 1.0))) (fma (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ -1 (fma (fabs x) 0.3275911 1.0)) (/ (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 2)) (fma (fabs x) 0.3275911 1.0)))))) (exp (- (* (fabs x) (fabs x))))))
4.7s
(log (/ (* 0.5 (* i (/ (/ (+ beta (+ i alpha)) (- (fma 2.0 i (+ beta alpha)) (sqrt 1.0))) (/ (fma 2.0 i (+ beta alpha)) i)))) (+ (sqrt 1.0) (fma 2.0 i (+ beta alpha)))))
3.1s
(* (/ (/ (fma i (+ (+ alpha i) beta) (* beta alpha)) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (+ (+ alpha i) beta) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (/ (fma 2.0 i (+ alpha beta)) i))))
1.8s
(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)

rewrite7.9m (25.2%)

Algorithm
159×rewrite-expression-head
Calls

485 calls:

1.2m
(* (* (sqrt (* PI 2.0)) (* (/ (pow (sqrt (- (+ (+ 7.0 z) 0.5) 1.0)) (+ (- z 1.0) 0.5)) (exp z)) (/ (pow (sqrt (- (+ (+ 7.0 z) 0.5) 1.0)) (+ (- z 1.0) 0.5)) (exp (- (- (- 1.0 0.5) 7.0)))))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ -0.13857109526572012 (+ 6.0 (- z 1.0))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))))
1.1m
(* (* (sqrt (* PI 2.0)) (/ (pow (- (+ 7.0 (+ z 0.5)) 1.0) (+ (- z 1.0) 0.5)) (exp (- z (- (- 1.0 0.5) 7.0))))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ -0.13857109526572012 (+ 6.0 (- z 1.0))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))))
1.1m
(* (/ (* (sqrt (* PI 2.0)) (pow (sqrt (+ (+ z 7.0) (- 0.5 1.0))) (* 2 (+ (- z 1.0) 0.5)))) (/ (exp z) (+ (/ -1259.1392167224028 (- (+ 2.0 z) 1.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 4.0 (- z 1.0)))) (/ 771.3234287776531 (+ 3.0 (- z 1.0)))) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0)))))))) (exp (- (- 1.0 0.5) 7.0)))
1.0m
(/ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z))) (+ (+ (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (/ -176.6150291621406 (+ (- z) 4.0)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))))) (exp (+ (+ 0.5 7.0) (- z))))
39.8s
(* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))
Rules
132869×times-frac
88723×*-un-lft-identity
53670×add-sqr-sqrt
51280×add-cube-cbrt
24459×sqrt-prod
20999×distribute-lft-out
4402×add-exp-log
4380×associate-/l*
3654×div-inv
3631×add-cbrt-cube
3326×pow1
2765×frac-add
2722×prod-diff
2413×prod-exp
2038×cbrt-unprod
1948×pow-prod-down
1601×associate-/r/
1463×associate-*r*
1401×flip-+ flip3-+
1123×unpow-prod-down
1043×exp-sum
931×associate-/r*
918×associate-*l*
806×distribute-lft-out--
796×difference-of-squares
782×div-exp
780×add-log-exp
610×associate-*r/
541×distribute-rgt-in distribute-lft-in
526×distribute-neg-in
486×expm1-log1p-u log1p-expm1-u
450×cbrt-undiv
355×associate--l+
344×cbrt-prod
342×pow-unpow
337×log-pow
327×cube-prod
304×frac-times
283×pow-exp
277×sqrt-pow1
256×unswap-sqr
230×associate-/l/
218×sqr-pow
170×associate-*l/
165×fma-def
162×pow-to-exp
146×associate-+l+
141×sum-log
138×sub-neg
133×flip-- flip3--
123×pow1/2
119×*-commutative
109×log-prod
108×frac-2neg clear-num
107×fma-neg
98×1-exp exp-prod
96×unpow-prod-up
83×sqrt-div
78×pow-pow
77×fma-udef
73×rec-exp
69×unpow3 cube-mult
65×pow1/3 swap-sqr
60×pow-prod-up
55×associate-+r+
49×diff-log
40×distribute-rgt-out
38×pow-sqr
36×+-commutative distribute-rgt-neg-in
33×distribute-lft-neg-in
25×pow-flip
23×rem-sqrt-square
22×rem-cube-cbrt
21×exp-diff
19×rem-log-exp div-sub
18×hypot-udef
17×associate--r-
13×cube-div
12×pow-div
11×frac-sub pow-plus inv-pow log-div
10×pow2
distribute-rgt-neg-out neg-mul-1
distribute-rgt1-in distribute-lft1-in sqrt-unprod rem-exp-log
un-div-inv exp-to-pow unpow2
associate-+r- cbrt-div count-2
associate--l- associate-+l- associate--r+
neg-sub0 sin-sum distribute-neg-frac cos-sum unsub-neg
expm1-log1p expm1-udef exp-neg rem-square-sqrt pow-sub
sqrt-undiv log1p-expm1 sum-cubes distribute-rgt-out-- distribute-frac-neg rem-cbrt-cube log1p-udef sqrt-pow2
difference-cubes hypot-def unpow1/3

prune5.2m (16.6%)

simplify4.5m (14.5%)

sample3.9m (12.5%)

Algorithm
100×intervals
Results
1.4m16169×body10240exit
54.5s459773×body80valid
32.9s31044×body1280valid
14.5s23726×body640valid
7.1s3116×body1280nan
6.4s69248×body80nan
4.5s11802×body320valid
3.6s2701×body640nan
3.4s10206×body160valid
1.7s49536×pre80true
1.5s1222×body320nan
1.3s1531×body2560valid
1.0s698×body160nan
351.0ms597×body5120valid

regimes14.0s (0.7%)

Accuracy

Total 27.4b remaining (23.6%)

Threshold costs 6.7b (5.8%)

7.4b34.8%_divideComplex, real part
4.7b40.1%Octave 3.8, jcobi/4
2.2b57.1%powComplex, imaginary part
2.1b55.2%powComplex, real part
2.0b0%Jmat.Real.lambertw, newton loop step

localize10.0s (0.5%)

bsearch1.4s (0.1%)

end1.0ms (0.0%)