Details

rewrite13.4m (37.5%)

Algorithm
153×rewrite-expression-head
Calls

443 calls:

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))))
57.2s
(log (exp (/ (+ (/ 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))))))
42.0s
(/ (+ (/ 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))))
7.8s
(+ (+ (+ (/ 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)))))
6.1s
(* (/ (+ (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (fma (* x x) 0.0001789971 0.0005064034)) (fma (* 0.0072644182 (* x x)) (* (* x x) (* x x)) (fma (* (* x x) (* x x)) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))) (fma (* 2.0 0.0001789971) (* (* (* x x) (* (* x x) (* x x))) (* (* x x) (* (* x x) (* x x)))) (fma (* (* x x) (* (* x x) (* x x))) (+ (* 0.0008327945 (* (* x x) (* x x))) (* (* x x) 0.0140005442)) (fma (* (* x x) (* (* x x) (* x x))) 0.0694555761 (fma 0.2909738639 (* (* x x) (* x x)) (fma (* x x) 0.7715471019 1.0)))))) x)
Rules
47206×frac-times
31206×associate-*r/
18311×associate-*l/
15184×exp-neg
14066×frac-add
13646×flip-+ flip3-+
13030×exp-diff
13018×neg-sub0
9538×*-un-lft-identity
8197×times-frac
7388×add-sqr-sqrt
5402×add-cube-cbrt
4040×pow1
3111×add-exp-log
2409×distribute-lft-out
2380×add-cbrt-cube
2188×un-div-inv
1891×sqrt-prod
1668×associate-*r*
1387×prod-diff
1369×pow-prod-up
1345×prod-exp
1164×associate-*l*
920×cbrt-unprod
881×pow-prod-down
841×add-log-exp
745×div-exp
681×pow-plus
533×difference-of-squares
530×unpow-prod-down
525×associate-/l*
447×associate-/r*
443×log1p-expm1-u
441×expm1-log1p-u div-inv
427×cube-prod
416×cbrt-undiv
372×distribute-lft-out--
365×pow-sqr
339×unswap-sqr
315×associate-/r/
302×swap-sqr
267×pow-exp
265×cbrt-prod
258×exp-sum
257×log-pow
250×pow2
238×associate-/l/
227×sum-log
222×sqr-pow
205×exp-prod
202×cbrt-div
185×fma-neg
175×fma-def
167×flip3-- flip--
163×*-commutative
151×1-exp
143×rec-exp
128×sqrt-div
117×pow-to-exp
101×unpow3 cube-mult
99×pow1/3
94×distribute-rgt-in distribute-lft-in
90×cube-div
81×frac-2neg clear-num
68×sub-neg
66×sqrt-pow1
61×cube-unmult
56×log-prod
55×pow1/2
52×fma-udef
48×diff-log
47×associate--l+
31×+-commutative
24×associate-+l+ pow-unpow distribute-rgt-out--
23×frac-sub
21×pow-pow distribute-rgt-out
20×rem-cube-cbrt div-sub
19×pow-flip
18×distribute-rgt1-in
17×rem-sqrt-square
15×pow3 distribute-rgt-neg-in
11×associate-+r+
inv-pow hypot-def
distribute-lft-neg-in associate--r+
cos-sum rem-exp-log
sin-sum neg-log associate--l- associate-+l- rem-log-exp
sqrt-unprod sub-div associate-+r- rem-square-sqrt rem-cbrt-cube unsub-neg log1p-udef
expm1-log1p expm1-udef log1p-expm1 difference-cubes hypot-udef
unpow-prod-up neg-mul-1 exp-to-pow distribute-neg-in associate--r- pow-sub log-div

simplify7.7m (21.6%)

prune6.0m (16.8%)

series5.2m (14.6%)

Calls

437 calls:

4.8s
(- (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))
4.3s
(+ (* (* (* (/ 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) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) 1)) (/ (sqrt (/ (+ (* 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))))
3.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))

sample3.0m (8.5%)

Algorithm
98×intervals
Results
53.2s11978×body10240exit
50.0s450253×body80valid
26.8s27048×body1280valid
12.5s21157×body640valid
6.8s70443×body80nan
5.1s10846×body320valid
3.1s1557×body1280nan
2.5s1342×body640nan
1.4s49536×pre80true
1.2s5664×body160valid
732.0ms1395×body2560valid
541.0ms693×body320nan
389.0ms616×body5120valid
181.0ms327×body160nan

regimes12.1s (0.6%)

Accuracy

Total 29.8b remaining (21.9%)

Threshold costs 4.7b (3.5%)

7.3b34%_divideComplex, imaginary part
6.4b-1.2%Octave 3.8, jcobi/2
3.3b-14.4%_divideComplex, real part
3.1b75.1%Octave 3.8, jcobi/1
2.3b36.3%Octave 3.8, jcobi/4

localize8.4s (0.4%)

bsearch1.8s (0.1%)

end1.0ms (0.0%)