Date:Thursday, August 20th, 2020
Commit:9dfd47eb on scaleup-plugins
Hostname:warfa with Racket 7.5
Seed:2020233
Parameters:256 points for 4 iterations
Flags:
setup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

prune4.2min (47.2%)

Filtered
35699 candidates to 30335 candidates (15.0%)

sample1.5min (17.6%)

Algorithm
60×intervals
Results
20.7s30728×body1280valid
14.0s159826×body80valid
9.6s20454×body640valid
6.8s7539×body2560valid
4.8s50779×body80nan
3.8s754×body5120invalid
3.4s1321×body2560invalid
3.3s10021×body320valid
2.7s4714×body1280nan
2.7s23988×body80invalid
2.2s2498×body5120valid
1.9s8870×body160valid
1.9s3676×body1280invalid
1.6s3895×body640nan
1.1s3019×body640invalid
613.0ms2012×body320nan
468.0ms1694×body320invalid
450.0ms646×body5120exit
338.0ms2540×body80overflowed
167.0ms848×body160invalid
164.0ms8256×pre80true
121.0ms668×body160nan

simplify1.1min (12.7%)

Algorithm
179×egg-herbie

series1.0min (11.7%)

Calls

451 calls:

2.5s
(+.f64 (*.f64 (+.f64 (pow.f64 (*.f64 b b) 6) (*.f64 (pow.f64 a 6) (pow.f64 (+.f64 (*.f64 a a) (*.f64 (*.f64 b b) 2)) 3))) (*.f64 (+.f64 1 (*.f64 a (+.f64 3 (*.f64 a 9)))) (-.f64 1 a))) (*.f64 (+.f64 (pow.f64 b 8) (*.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (pow.f64 b 4)))) (*.f64 4 (+.f64 (*.f64 (*.f64 (*.f64 a a) (-.f64 1 (*.f64 a a))) (+.f64 1 (*.f64 a (+.f64 3 (*.f64 a 9))))) (*.f64 (*.f64 (*.f64 b b) (-.f64 1 (pow.f64 (*.f64 a 3) 3))) (-.f64 1 a))))))
2.4s
(sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (+.f64 (*.f64 l -2) (*.f64 n (*.f64 (/.f64 l Om) (-.f64 U* U))))))))
2.3s
(sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (+.f64 (*.f64 l -2) (*.f64 n (*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 l Om) (-.f64 U* U))) (cbrt.f64 (*.f64 (/.f64 l Om) (-.f64 U* U)))) (cbrt.f64 (*.f64 (/.f64 l Om) (-.f64 U* U))))))))))
2.2s
(sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (+.f64 (*.f64 l -2) (*.f64 n (*.f64 (/.f64 l Om) (-.f64 U* U)))))))) (cbrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (+.f64 (*.f64 l -2) (*.f64 n (*.f64 (/.f64 l Om) (-.f64 U* U))))))))) (cbrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (+.f64 (*.f64 l -2) (*.f64 n (*.f64 (/.f64 l Om) (-.f64 U* U))))))))))
1.3s
(/.f64 (+.f64 (*.f64 (+.f64 (pow.f64 (*.f64 b b) 6) (*.f64 (pow.f64 a 6) (pow.f64 (+.f64 (*.f64 a a) (*.f64 (*.f64 b b) 2)) 3))) (*.f64 (+.f64 1 (*.f64 a (+.f64 3 (*.f64 a 9)))) (-.f64 1 a))) (*.f64 (+.f64 (pow.f64 b 8) (*.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (pow.f64 b 4)))) (*.f64 4 (+.f64 (*.f64 (*.f64 (*.f64 a a) (-.f64 1 (*.f64 a a))) (+.f64 1 (*.f64 a (+.f64 3 (*.f64 a 9))))) (*.f64 (*.f64 (*.f64 b b) (-.f64 1 (pow.f64 (*.f64 a 3) 3))) (-.f64 1 a)))))) (*.f64 (+.f64 (pow.f64 b 8) (*.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (pow.f64 b 4)))) (*.f64 (+.f64 1 (*.f64 a (+.f64 3 (*.f64 a 9)))) (-.f64 1 a))))

analyze34.4s (6.5%)

Algorithm
31×search
Search
TrueOtherFalseIter
0%98.2%1.8%0
3.2%95%1.8%1
5.6%91%3.4%2
8%84.5%7.4%3
9.8%80.7%9.5%4
13.5%76.9%9.7%5
16%72.8%11.2%6
18.1%68.2%13.7%7
21.2%62.6%16.2%8
24.7%57%18.2%9
26.4%53.6%20%10
28.9%49.8%21.3%11
30.2%47.2%22.5%12
31.9%42.5%25.7%13
32.9%40.8%26.3%14

rewrite14.1s (2.7%)

Algorithm
119×rewrite-expression-head
Calls

451 calls:

754.0ms
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 b 8) (*.f64 (pow.f64 a 4) (*.f64 (+.f64 (*.f64 a a) (*.f64 (*.f64 b b) 2)) (+.f64 (*.f64 a a) (*.f64 (*.f64 b b) 2)))))) (*.f64 (+.f64 (*.f64 a (*.f64 (-.f64 a (pow.f64 a 3)) (-.f64 3 a))) (*.f64 (*.f64 (*.f64 b b) (-.f64 9 (*.f64 a a))) (+.f64 a 1))) (*.f64 4 (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)))))) (*.f64 (*.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)))))
494.0ms
(/.f64 (+.f64 (*.f64 (+.f64 (pow.f64 (*.f64 b b) 6) (*.f64 (pow.f64 a 6) (pow.f64 (+.f64 (*.f64 a a) (*.f64 (*.f64 b b) 2)) 3))) (*.f64 (+.f64 1 (*.f64 a (+.f64 3 (*.f64 a 9)))) (-.f64 1 a))) (*.f64 (+.f64 (pow.f64 b 8) (*.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (pow.f64 b 4)))) (*.f64 4 (+.f64 (*.f64 (*.f64 (*.f64 a a) (-.f64 1 (*.f64 a a))) (+.f64 1 (*.f64 a (+.f64 3 (*.f64 a 9))))) (*.f64 (*.f64 (*.f64 b b) (-.f64 1 (pow.f64 (*.f64 a 3) 3))) (-.f64 1 a)))))) (*.f64 (+.f64 (pow.f64 b 8) (*.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (pow.f64 b 4)))) (*.f64 (+.f64 1 (*.f64 a (+.f64 3 (*.f64 a 9)))) (-.f64 1 a))))
175.0ms
(+.f64 (*.f64 (*.f64 (-.f64 3 a) (+.f64 a 1)) (-.f64 (pow.f64 b 8) (*.f64 (pow.f64 a 4) (*.f64 (+.f64 (*.f64 a a) (*.f64 (*.f64 b b) 2)) (+.f64 (*.f64 a a) (*.f64 (*.f64 b b) 2)))))) (*.f64 (+.f64 (*.f64 a (*.f64 (-.f64 a (pow.f64 a 3)) (-.f64 3 a))) (*.f64 (*.f64 (*.f64 b b) (-.f64 9 (*.f64 a a))) (+.f64 a 1))) (*.f64 4 (-.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2))))))
167.0ms
(+.f64 (*.f64 (+.f64 (pow.f64 (*.f64 b b) 6) (*.f64 (pow.f64 a 6) (pow.f64 (+.f64 (*.f64 a a) (*.f64 (*.f64 b b) 2)) 3))) (*.f64 (+.f64 1 (*.f64 a (+.f64 3 (*.f64 a 9)))) (-.f64 1 a))) (*.f64 (+.f64 (pow.f64 b 8) (*.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (-.f64 (+.f64 (pow.f64 a 4) (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2)) (pow.f64 b 4)))) (*.f64 4 (+.f64 (*.f64 (*.f64 (*.f64 a a) (-.f64 1 (*.f64 a a))) (+.f64 1 (*.f64 a (+.f64 3 (*.f64 a 9))))) (*.f64 (*.f64 (*.f64 b b) (-.f64 1 (pow.f64 (*.f64 a 3) 3))) (-.f64 1 a))))))
100.0ms
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
Rules
73043×associate-*r/_binary64
56782×frac-times_binary64
40825×frac-add_binary64
37108×flip3--_binary64 flip--_binary64
22834×associate-*l/_binary64
22416×flip3-+_binary64 flip-+_binary64
10471×associate-/l/_binary64
4744×times-frac_binary64
4585×add-exp-log_binary64
4310×add-sqr-sqrt_binary64
4164×*-un-lft-identity_binary64
3274×add-cbrt-cube_binary64
3141×add-cube-cbrt_binary64
2054×prod-exp_binary64
1576×sqrt-prod_binary64
1397×cbrt-unprod_binary64
1377×pow1_binary64
1051×div-exp_binary64
905×associate-*r*_binary64
709×sqrt-div_binary64
676×cbrt-undiv_binary64
657×unpow-prod-down_binary64
637×associate-*l*_binary64
569×add-log-exp_binary64
475×pow-prod-down_binary64
455×associate-/l*_binary64
438×cbrt-prod_binary64
420×associate-/r*_binary64
396×distribute-lft-out_binary64
378×associate-/r/_binary64
331×cbrt-div_binary64
330×div-inv_binary64
282×difference-of-squares_binary64
264×unswap-sqr_binary64
222×pow-exp_binary64
216×sqr-pow_binary64
151×*-commutative_binary64
146×distribute-lft-out--_binary64
138×pow-to-exp_binary64
132×sqrt-pow1_binary64
127×pow-unpow_binary64
103×clear-num_binary64 frac-2neg_binary64
101×tan-quot_binary64
84×pow1/2_binary64
78×rem-sqrt-square_binary64
74×cube-prod_binary64
73×distribute-rgt-in_binary64 distribute-lft-in_binary64
70×unpow2_binary64
69×sub-neg_binary64
62×log-prod_binary64
49×sum-log_binary64
44×pow-pow_binary64
41×pow1/3_binary64
39×1-exp_binary64
28×+-commutative_binary64
25×associate-+r+_binary64 div-sub_binary64
21×rec-exp_binary64
20×pow-prod-up_binary64
18×cube-div_binary64
16×diff-log_binary64 unpow3_binary64 cube-mult_binary64 pow-plus_binary64
14×log-pow_binary64
11×frac-sub_binary64 exp-diff_binary64
10×associate-+l+_binary64 pow-sqr_binary64
swap-sqr_binary64 rem-log-exp_binary64 difference-of-sqr-1_binary64 exp-prod_binary64
pow-flip_binary64 pow2_binary64
inv-pow_binary64 rem-cube-cbrt_binary64
acos-asin_binary64 distribute-rgt-out--_binary64
sinh-def_binary64 exp-sum_binary64 sub-div_binary64
rem-cbrt-cube_binary64 distribute-lft-neg-in_binary64 distribute-rgt-neg-in_binary64 cos-diff_binary64 log-div_binary64 cos-sum_binary64 un-div-inv_binary64 associate--l+_binary64
sqrt-unprod_binary64 sqrt-undiv_binary64 distribute-rgt-out_binary64 sinh-undef_binary64 sin-mult_binary64 pow-sub_binary64 asin-acos_binary64
associate--r+_binary64 sqrt-pow2_binary64 pow3_binary64 neg-mul-1_binary64 exp-to-pow_binary64 rem-exp-log_binary64 sqr-sin-a_binary64 mul0-rgt_binary64

regimes5.2s (1.0%)

Accuracy

Total 40.3b remaining (21%)

Threshold costs 4.0b (2.1%)

8.7b39.1%Henrywood and Agarwal, Equation (3)
7.5b0.1%Henrywood and Agarwal, Equation (12)
5.5b76.7%Toniolo and Linder, Equation (7)
4.5b50.2%Toniolo and Linder, Equation (13)
3.5b49%Toniolo and Linder, Equation (10+)

localize2.1s (0.4%)

bsearch1.8s (0.3%)

end1.0ms (0.0%)

Profiling

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