Details

sample10.3m (32.5%)

Algorithm
96×intervals
Results
6.9m107018×body10240exit
1.3m419088×body80valid
33.7s26442×body1280valid
18.9s20592×body640valid
12.1s70130×body80nan
10.4s3089×body1280nan
6.9s2598×body640nan
6.8s10795×body320valid
3.4s9654×body160valid
3.2s49536×pre80true
2.2s1320×body320nan
1.8s1456×body2560valid
692.0ms601×body5120valid
653.0ms694×body160nan

simplify7.4m (23.3%)

prune6.0m (19.1%)

series4.4m (14.1%)

Calls

496 calls:

2.9m
(- (pow (pow 1 3) 3) (pow (* (sqrt (pow (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) 3)) (sqrt (pow (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) 3))) 3))
4.6s
(- (pow 1 3) (pow (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) 3))
4.0s
(- (pow 1 3) (* (sqrt (pow (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) 3)) (sqrt (pow (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) 3))))
3.2s
(+ (* (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911))))) (* 1 (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911))))))
3.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))

rewrite3.1m (9.7%)

Algorithm
154×rewrite-expression-head
Calls

496 calls:

24.4s
(* (* (/ 1 (sqrt (* (cbrt (exp (+ (+ 7 (- z 1)) 0.5))) (cbrt (exp (+ (+ 7 (- z 1)) 0.5)))))) (* (/ (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (cbrt (exp (+ (+ 7 (- z 1)) 0.5))))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (+ 7 (- z 1)) 0.5)))))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (+ (/ 12.507343278686905 (+ z 4)) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))))) (+ (+ (/ -176.6150291621406 (+ (- z 1) 4)) (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z))))) (/ -1259.1392167224028 (+ 1 z)))))
18.1s
(* (/ (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (+ 7 (- z 1)) 0.5))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (+ (/ 12.507343278686905 (+ z 4)) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))))) (+ (+ (/ -176.6150291621406 (+ (- z 1) 4)) (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z))))) (/ -1259.1392167224028 (+ 1 z)))))
17.6s
(* (* (/ (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (exp (+ (+ 7 (- z 1)) 0.5)))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (+ 7 (- z 1)) 0.5))))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (+ (/ 12.507343278686905 (+ z 4)) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))))) (+ (+ (/ -176.6150291621406 (+ (- z 1) 4)) (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z))))) (/ -1259.1392167224028 (+ 1 z)))))
16.7s
(* (* 1 (* (/ (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (cbrt (exp (+ (+ 7 (- z 1)) 0.5))))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (+ 7 (- z 1)) 0.5)))))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (+ (/ 12.507343278686905 (+ z 4)) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))))) (+ (+ (/ -176.6150291621406 (+ (- z 1) 4)) (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z))))) (/ -1259.1392167224028 (+ 1 z)))))
9.6s
(* (/ (+ (* (- (* (* (* (* x x) (* x x)) (+ 0.0424060604 (* (* (* x x) (* x x)) (+ 0.0005064034 (* (* x x) 0.0001789971))))) (* (* (* x x) (* x x)) (+ 0.0424060604 (* (* (* x x) (* x x)) (+ 0.0005064034 (* (* x x) 0.0001789971)))))) (* 1 1)) (- (* (* (* x x) (* x x)) 0.0072644182) 0.1049934947)) (* (- (* (* (* x x) (* x x)) (+ 0.0424060604 (* (* (* x x) (* x x)) (+ 0.0005064034 (* (* x x) 0.0001789971))))) 1) (* (* x x) (- (* (* (* (* x x) (* x x)) 0.0072644182) (* (* (* x x) (* x x)) 0.0072644182)) (* 0.1049934947 0.1049934947))))) (* (+ (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (+ (* 0.0001789971 (* 2 (* (* x x) (* x x)))) (+ 0.0140005442 (* 0.0008327945 (* x x))))) (+ (* (* x x) (+ 0.7715471019 (* 0.0694555761 (* (* x x) (* x x))))) (+ 1 (* 0.2909738639 (* (* x x) (* x x)))))) (* (- (* (* (* x x) (* x x)) (+ 0.0424060604 (* (* (* x x) (* x x)) (+ 0.0005064034 (* (* x x) 0.0001789971))))) 1) (- (* (* (* x x) (* x x)) 0.0072644182) 0.1049934947)))) x)
Rules
12448×*-un-lft-identity
9793×times-frac
6688×add-sqr-sqrt
4835×add-cube-cbrt
4251×distribute-lft-out
3419×pow1
3000×frac-add
2995×add-exp-log
2367×add-cbrt-cube
1899×associate-*l*
1843×frac-times
1785×flip-+ flip3-+
1714×associate-*r*
1546×associate-*r/
1270×sqrt-prod
1194×prod-exp
973×pow-prod-up
923×associate-*l/
919×cbrt-prod
896×associate-/r/
887×cbrt-unprod
760×add-log-exp
753×pow-prod-down
654×div-exp
565×associate-/l*
560×cbrt-div
530×pow-plus
524×sqrt-div
496×insert-posit16
490×flip3-- flip--
465×difference-of-squares
454×cbrt-undiv
403×associate-/r*
397×unpow-prod-down
383×unswap-sqr
367×div-inv
320×pow-sqr
283×distribute-lft-out--
231×swap-sqr
206×pow2
185×associate-/l/
180×*-commutative
153×sqrt-pow1
151×pow1/3
135×sqr-pow
134×cube-prod
117×log-pow
93×pow1/2
88×pow-exp
87×frac-2neg clear-num
76×exp-sum
75×sub-neg
72×diff-log
71×sum-log
67×1-exp
62×log-prod distribute-rgt-in distribute-lft-in
58×rem-sqrt-square
57×pow-to-exp
46×rec-exp +-commutative
37×pow-unpow
36×associate--l+
33×unpow-prod-up
31×pow3
29×distribute-rgt-out
28×distribute-rgt1-in
27×cube-unmult
23×associate-+l-
22×frac-sub exp-prod
19×exp-diff associate-+r-
18×rem-cube-cbrt div-sub
15×pow-flip pow-pow
11×associate--l-
10×difference-of-sqr-1
associate-+l+ inv-pow rem-exp-log log-div
associate--r+
un-div-inv cube-mult
sin-sum associate-+r+ unpow3 cube-div
pow-sub
rem-log-exp
sqrt-undiv exp-to-pow
remove-posit16 sub0-neg sqrt-unprod difference-cubes unpow1/3 associate--r-
rem-square-sqrt cos-sum rem-cbrt-cube unsub-neg

regimes13.2s (0.7%)

Accuracy

Total 92.4b remaining (36.6%)

Threshold costs 3.8b (1.5%)

10.6b50.4%math.log/2 on complex, real part
10.3b56.6%math.log10 on complex, real part
10.1b57.2%math.log/1 on complex, real part
8.9b59.4%math.abs on complex
8.8b42.2%Octave 3.8, jcobi/4

localize8.1s (0.4%)

bsearch4.5s (0.2%)

end1.0ms (0.0%)