Date:Sunday, May 10th, 2020
Commit:c1e4db38 on master
Hostname:warfa with Racket 7.5
Seed:2020131
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

sample2.2m (35.6%)

Algorithm
100×intervals
Results
46.5s7920×body5120exit
31.1s529990×body80valid
16.0s30481×body1280valid
7.8s23873×body640valid
4.0s3121×body1280nan
3.3s70835×body80nan
2.8s12081×body320valid
2.5s2670×body640nan
1.5s10156×body160valid
928.0ms49536×pre80true
872.0ms1303×body320nan
871.0ms8036×body80overflowed
455.0ms1460×body2560valid
276.0ms653×body160nan
189.0ms562×body5120valid

prune2.1m (33.0%)

Filtered
45483 candidates to 24279 candidates (53.4%)

series1.0m (16.8%)

Calls

489 calls:

2.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
2.3s
(* (/ (/ (* 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))))
932.0ms
(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 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))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ z 6.5))))
826.0ms
(- 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 (neg (* (fabs x) (fabs x))))))
782.0ms
(* (* (* (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))))

simplify29.6s (7.9%)

Algorithm
262×egg-herbie

rewrite12.8s (3.4%)

Algorithm
162×rewrite-expression-head
Calls

489 calls:

649.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
152.0ms
(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 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))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ z 6.5))))
149.0ms
(* (* (* (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))))
141.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ z 6.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 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))))
135.0ms
(* (+ (+ (+ (+ (+ (+ (+ (+ 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))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)))
Rules
159408×times-frac
86868×*-un-lft-identity
59856×add-sqr-sqrt
58439×add-cube-cbrt
25420×sqrt-prod
14094×distribute-lft-out
3300×associate-/r/
3140×div-inv
2579×add-exp-log
2148×flip-+ flip3-+
2013×add-cbrt-cube
1601×associate-*r*
1588×pow1
1228×frac-add
1100×associate-*l*
847×prod-exp
838×associate-*r/
814×add-log-exp
731×associate-/r*
708×associate-/l*
653×div-exp
625×cbrt-unprod
499×frac-times
396×cbrt-undiv
376×pow-prod-down
370×unswap-sqr
363×unpow-prod-down
302×cbrt-div
270×log-pow
263×sqrt-div
261×difference-of-squares
235×cbrt-prod
233×flip-- flip3--
222×associate-*l/
197×distribute-lft-out--
190×cube-prod
183×swap-sqr
173×sqrt-pow1
154×*-commutative
146×sqr-pow
129×log-prod
127×associate-/l/
121×pow-exp
120×pow1/2
108×associate-+l-
107×pow-sub
105×exp-neg
102×pow-to-exp
98×sum-log
97×exp-prod
95×pow1/3
93×distribute-rgt-in distribute-lft-in
89×sub-neg
82×diff-log
78×clear-num frac-2neg
76×exp-diff
73×pow-unpow
71×neg-sub0
70×pow-prod-up
69×1-exp
61×rem-sqrt-square
55×+-commutative
49×rec-exp
46×pow-sqr
43×un-div-inv
38×associate--l+
37×pow-plus pow-pow
31×unpow3 cube-mult
29×pow2
22×unpow2
21×associate-+r+
18×associate-+l+ rem-exp-log div-sub
17×rem-cube-cbrt
16×distribute-lft-neg-in exp-sum distribute-rgt-neg-in
13×rem-log-exp log-div
11×cube-div associate--l-
10×neg-log
inv-pow pow-flip
cos-sum
associate--r+
unpow-prod-up
sin-sum
distribute-neg-in distribute-rgt-out-- distribute-rgt-out neg-mul-1 frac-sub
sqrt-pow2 sqrt-unprod pow3 rem-square-sqrt rem-cbrt-cube
distribute-lft1-in associate-+r- distribute-rgt1-in sub-div count-2 sum-cubes

regimes7.5s (2.0%)

Accuracy

Total 83.0b remaining (30%)

Threshold costs 5.3b (1.9%)

11.2b46.1%math.sqrt on complex, real part
10.9b55.1%math.log/2 on complex, real part
10.5b56.4%math.log10 on complex, real part
10.3b56.8%math.log/1 on complex, real part
9.9b57.5%math.abs on complex

localize2.6s (0.7%)

bsearch2.0s (0.5%)

end1.0ms (0.0%)

Profiling

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