Details

simplify24.7m (54.8%)

prune8.1m (18.0%)

sample5.0m (11.2%)

Algorithm
99×intervals
Results
1.6m15671×body10240exit
1.2m439811×body80valid
45.0s30626×body1280valid
22.8s23542×body640valid
11.2s3114×body1280nan
10.6s71349×body80nan
7.9s2508×body640nan
6.5s11733×body320valid
3.5s10035×body160valid
3.3s49536×pre80true
2.6s1251×body320nan
1.4s1473×body2560valid
1.1s640×body160nan
608.0ms632×body5120valid

series4.1m (9.2%)

Calls

434 calls:

2.4m
(- (pow (pow 1 3) 3) (pow (* (sqrt (pow (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3)) (sqrt (pow (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3))) 3))
5.8s
(+ (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) (* 1.0 (* 1.0 1.0)))
5.7s
(+ (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) (* 1.0 (* 1.0 1.0)))
4.2s
(- (pow 1 3) (pow (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3))
3.8s
(+ (* (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))) (* 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))

rewrite2.8m (6.2%)

Algorithm
152×rewrite-expression-head
Calls

434 calls:

18.2s
(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
18.0s
(* (exp (- -6 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
17.9s
(* (exp (- -6 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
15.9s
(* (/ (+ (+ (+ (+ (+ 1 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x)
15.2s
(* (* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (exp (+ (- z -6) 0.5)))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (- z -6) 0.5))))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
Rules
55870×*-un-lft-identity
49827×times-frac
26155×add-exp-log
25801×frac-times
22249×distribute-lft-out
20300×add-sqr-sqrt
18486×add-cube-cbrt
17986×prod-exp
16982×associate-*r/
11621×sqrt-prod
10511×frac-add
9798×associate-*l/
8955×div-exp
8954×flip-+ flip3-+
7882×exp-neg
7179×exp-diff
6756×neg-sub0
4885×pow1
4301×1-exp
4294×rec-exp
2640×add-cbrt-cube
1977×prod-diff
1923×associate-/l*
1853×pow-prod-up
1400×associate-/r/
1180×un-div-inv
1166×associate-*r*
1128×pow-exp
1113×associate-*l*
1107×cbrt-unprod
1075×pow-to-exp
1035×div-inv
943×pow-prod-down
821×pow-plus
710×unpow-prod-up
678×difference-of-squares
560×associate-/r*
555×add-log-exp
505×pow-sqr
491×cbrt-undiv
489×cbrt-prod
449×unpow-prod-down
438×expm1-log1p-u
437×log1p-expm1-u
434×insert-posit16
400×exp-sum
362×distribute-lft-out--
344×pow2
340×unswap-sqr
307×log-pow
303×cube-prod
254×distribute-rgt-in distribute-lft-in
228×sqrt-div
186×swap-sqr
178×fma-neg
175×sqr-pow
165×*-commutative
163×associate--l+
159×log-prod
148×sqrt-pow1
145×flip3-- flip--
137×pow-flip
131×inv-pow
126×fma-def
108×cube-div
92×frac-sub sub-neg
87×frac-2neg clear-num cube-mult
86×unpow3
83×associate-/l/
76×pow1/3
66×pow1/2
62×cube-unmult
53×fma-udef
47×cbrt-div
37×pow-unpow
36×diff-log
32×distribute-rgt-out
29×sum-log
24×rem-cube-cbrt pow-pow
23×exp-prod
22×rem-sqrt-square
19×distribute-rgt1-in +-commutative
15×associate--r-
14×associate-+l-
pow3
log1p-expm1 pow-sub associate--r+ hypot-def log1p-udef
associate-+l+ distribute-lft1-in div-sub cos-sum count-2
sqrt-unprod
expm1-log1p expm1-udef sin-sum
rem-log-exp rem-exp-log
remove-posit16 associate-+r+ difference-cubes sum-cubes rem-square-sqrt log-div
associate--l-

regimes9.4s (0.3%)

Accuracy

Total 33.9b remaining (25.1%)

Threshold costs 7.9b (5.9%)

7.6b35.5%_divideComplex, real part
7.0b33.9%_divideComplex, imaginary part
5.5b13.3%Octave 3.8, jcobi/2
3.1b76.4%Octave 3.8, jcobi/1
1.5b44.8%Octave 3.8, jcobi/4

localize8.2s (0.3%)

bsearch1.7s (0.1%)

end1.0ms (0.0%)