Date:Friday, May 29th, 2020
Commit:30d0df99 on master
Hostname:warfa with Racket 7.5
Seed:2020150
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

sample2.3m (44.2%)

Algorithm
100×intervals
Results
48.8s7896×body5120exit
24.9s444328×body80valid
17.5s30730×body1280valid
8.7s23668×body640valid
5.2s3164×body1280nan
3.6s69741×body80nan
3.2s2635×body640nan
2.8s12003×body320valid
1.9s9898×body160valid
1.1s1285×body320nan
1.1s8092×body80overflowed
862.0ms49536×pre80true
448.0ms1447×body2560valid
350.0ms628×body160nan
205.0ms615×body5120valid

prune1.5m (29.7%)

Filtered
19250 candidates to 11610 candidates (39.7%)

series43.3s (13.8%)

Calls

472 calls:

7.4s
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 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))))))) (* (/ 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))))))))) (- 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 (neg (* (fabs x) (fabs x))))) 3))
7.2s
(- (pow 1.0 3) (/ (pow (* 1.0 (- (* 0.254829592 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))))))) (* (/ 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)))))))))) 3) (pow (* (* (+ 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)))
6.6s
(log (+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3)))
2.9s
(exp (log (+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))))
2.9s
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))

simplify15.4s (4.9%)

Algorithm
257×egg-herbie

regimes11.7s (3.7%)

Accuracy

Total 105.7b remaining (42.3%)

Threshold costs 6.1b (2.4%)

20.9b44.3%math.sqrt on complex, imaginary part, im greater than 0 branch
11.9b27.1%Octave 3.8, jcobi/4
10.1b58.8%math.log/2 on complex, real part
10.1b59.5%math.log10 on complex, real part
10.0b59.7%math.log/1 on complex, real part

rewrite7.7s (2.5%)

Algorithm
157×rewrite-expression-head
Calls

472 calls:

1.6s
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
248.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
142.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
108.0ms
(* (/ (/ (+ (+ (* (* (pow x 2) (* (pow x 2) (* (pow x 2) (* x (pow x 3))))) 0.0001789971) (+ (+ (* (* (pow x 2) (* x (pow x 3))) 0.0072644182) 1.0) (* (pow x 2) (+ 0.1049934947 (* 0.0424060604 (pow x 2)))))) (* (* (pow x 2) (* (pow x 2) (* x (pow x 3)))) 0.0005064034)) (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* 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 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))))) (sqrt (+ (+ (+ (+ (+ (+ 1.0 (* 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 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))))) x)
100.0ms
(* (/ (/ (* 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))))
Rules
12442×times-frac
9183×*-un-lft-identity
8779×add-sqr-sqrt
6476×add-cube-cbrt
4313×sqrt-prod
2910×add-exp-log
2384×add-cbrt-cube
2141×associate-*r*
2066×pow1
1638×associate-*l*
1169×distribute-lft-out
1079×prod-exp
855×flip-+ flip3-+
834×cbrt-unprod
725×add-log-exp
721×associate-/r/
647×div-exp
640×frac-times
587×associate-*r/
548×unswap-sqr
537×associate-/r*
533×pow-prod-down
514×associate-/l*
505×unpow-prod-down
482×cbrt-undiv
468×div-inv
432×frac-add
389×cbrt-prod
384×sqrt-div
377×log-pow
374×associate-*l/
309×difference-of-squares
296×sqrt-pow1
222×swap-sqr
200×distribute-lft-out--
197×pow-unpow
193×pow1/2
172×pow-prod-up
171×*-commutative
168×cbrt-div
167×sqr-pow
164×log-prod
153×pow-exp
130×flip-- flip3--
115×pow-sqr
113×distribute-rgt-in distribute-lft-in
99×associate-/l/
82×pow-plus
79×pow-to-exp frac-2neg pow1/3 clear-num
78×cube-prod
76×exp-neg sub-neg
71×sum-log
70×1-exp
67×diff-log
65×exp-diff rem-sqrt-square
63×rec-exp
60×neg-sub0
56×associate-+l-
53×pow-sub pow2
50×exp-prod
42×exp-sum
41×+-commutative
32×associate--l+
24×un-div-inv log-div
20×frac-sub
18×div-sub
17×unpow3 cube-mult
15×pow-pow
14×rem-exp-log pow-flip distribute-rgt-neg-in
12×cube-div distribute-lft-neg-in inv-pow associate--r+
11×rem-log-exp
10×associate-+l+
neg-log rem-cube-cbrt
associate--l- sqrt-unprod
associate-+r+
sin-sum unpow2
pow-div sum-cubes sub-div
cos-sum
pow3 distribute-neg-in unpow-prod-up rem-square-sqrt neg-mul-1 rem-cbrt-cube exp-to-pow
sqrt-undiv difference-cubes sqrt-pow2 associate-+r- unsub-neg

localize2.7s (0.9%)

bsearch861.0ms (0.3%)

end1.0ms (0.0%)

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