Date:Tuesday, July 28th, 2020
Commit:32b35f01 on refactor-reprify
Hostname:warfa with Racket 7.5
Seed:2020210
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

sample7.6min (41.6%)

Algorithm
417×intervals
Results
1.9min200272×body1280valid
1.3min17942×body5120exit
1.1min1164935×body80valid
41.6s128829×body640valid
29.7s35892×body2560valid
15.2s77736×body320valid
11.4s82371×body160valid
8.1s379072×pre80true
7.8s15757×body1280invalid
6.1s67548×body80invalid
5.8s12127×body1280nan
5.6s68718×body80nan
4.4s2313×body1280overflowed
4.3s12814×body640invalid
3.7s1504×body2560invalid
3.6s768×body5120invalid
3.3s9234×body640nan
3.3s18717×body80overflowed
2.7s4137×body5120valid
2.0s1762×body640overflowed
1.5s6404×body320invalid
1.1s4683×body320nan
592.0ms918×body320overflowed
581.0ms3033×body2560nan
487.0ms3149×body160invalid
270.0ms1821×body160nan
165.0ms449×body160overflowed
109.0ms163×body2560overflowed
6.0ms232×pre80false

prune4.0min (22.0%)

Filtered
93582 candidates to 68092 candidates (27.2%)

analyze2.2min (11.9%)

Algorithm
209×search
random
Search
TrueOtherFalseIter
0%81.8%18.2%0
4.2%77.6%18.2%1
8.6%72%19.4%2
18.7%59.5%21.8%3
23.6%52.4%24.1%4
29.5%45.5%25%5
32.4%41.2%26.4%6
35.4%36.4%28.3%7
37.7%33.1%29.2%8
40.4%29.4%30.2%9
42.1%26.8%31.1%10
43.6%24.6%31.8%11
45.1%22.5%32.4%12
47%19.7%33.3%13
47.7%18.7%33.7%14

simplify1.6min (8.8%)

Algorithm
1129×egg-herbie

series1.2min (6.6%)

Calls

2281 calls:

2.5s
(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (*.f64 (-.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
2.4s
(sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (*.f64 (-.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
1.4s
(+.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 (pow.f64 a 4) (*.f64 (-.f64 1 a) (-.f64 1 a))) (*.f64 b (*.f64 (*.f64 b (+.f64 a 3)) (-.f64 (*.f64 (*.f64 b b) (+.f64 a 3)) (*.f64 (*.f64 a a) (-.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 (pow.f64 (*.f64 (*.f64 b b) (+.f64 a 3)) 3) (pow.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) 3)))))
1.3s
(-.f64 1 (*.f64 (sqrt.f64 (pow.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (*.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) 3)) (sqrt.f64 (pow.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (*.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) 3))))
1.2s
(-.f64 1 (*.f64 (sqrt.f64 (pow.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (*.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) 3)) (sqrt.f64 (*.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 3) (pow.f64 (/.f64 (sqrt.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (exp.f64 (pow.f64 (fabs.f64 x) 2))) 3)))))

regimes48.2s (4.4%)

Accuracy

Total 217.8b remaining (25.3%)

Threshold costs 29.3b (3.4%)

10.7b55%math.abs on complex
10.4b57.1%math.log/2 on complex, real part
10.3b57.5%math.log10 on complex, real part
10.2b58%math.log/1 on complex, real part
9.7b48.9%math.sqrt on complex, imaginary part, im greater than 0 branch

rewrite36.0s (3.3%)

Algorithm
716×rewrite-expression-head
Calls

2281 calls:

1.0s
(/.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 (pow.f64 a 4) (*.f64 (-.f64 1 a) (-.f64 1 a))) (*.f64 b (*.f64 (*.f64 b (+.f64 a 3)) (-.f64 (*.f64 (*.f64 b b) (+.f64 a 3)) (*.f64 (*.f64 a a) (-.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 (pow.f64 (*.f64 (*.f64 b b) (+.f64 a 3)) 3) (pow.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) 3))))) (*.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 (pow.f64 a 4) (*.f64 (-.f64 1 a) (-.f64 1 a))) (*.f64 b (*.f64 (*.f64 b (+.f64 a 3)) (-.f64 (*.f64 (*.f64 b b) (+.f64 a 3)) (*.f64 (*.f64 a a) (-.f64 1 a))))))))
298.0ms
(+.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 (pow.f64 a 4) (*.f64 (-.f64 1 a) (-.f64 1 a))) (*.f64 b (*.f64 (*.f64 b (+.f64 a 3)) (-.f64 (*.f64 (*.f64 b b) (+.f64 a 3)) (*.f64 (*.f64 a a) (-.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 (pow.f64 (*.f64 (*.f64 b b) (+.f64 a 3)) 3) (pow.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) 3)))))
158.0ms
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (*.f64 1737369620307813/2251799813685248 (*.f64 x x))) (*.f64 2620859570069187/9007199254740992 (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 2502400853142105/36028797018963968 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)))) (*.f64 2017691060547333/144115188075855872 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 7681173503746455/9223372036854775808 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 (*.f64 2 825478423409049/4611686018427387904) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x))))) (cbrt.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (*.f64 1737369620307813/2251799813685248 (*.f64 x x))) (*.f64 2620859570069187/9007199254740992 (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 2502400853142105/36028797018963968 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)))) (*.f64 2017691060547333/144115188075855872 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 7681173503746455/9223372036854775808 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 (*.f64 2 825478423409049/4611686018427387904) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x))))))) (*.f64 x (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (*.f64 3782789308857969/36028797018963968 (*.f64 x x))) (*.f64 763919671262763/18014398509481984 (pow.f64 x 4))) (*.f64 8375303961237363/1152921504606846976 (pow.f64 x 6))) (*.f64 583843369866023/1152921504606846976 (pow.f64 x 8))) (*.f64 825478423409049/4611686018427387904 (pow.f64 x 10))) (cbrt.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (*.f64 (*.f64 x x) 1737369620307813/2251799813685248)) (*.f64 (pow.f64 x 4) 2620859570069187/9007199254740992)) (*.f64 (pow.f64 x 6) 2502400853142105/36028797018963968)) (*.f64 (pow.f64 x 8) 2017691060547333/144115188075855872)) (*.f64 (pow.f64 x 10) 7681173503746455/9223372036854775808)) (*.f64 825478423409049/2305843009213693952 (pow.f64 x 12)))))))
108.0ms
(/.f64 (+.f64 (*.f64 (+.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 x1 (*.f64 x1 3)) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6) (*.f64 (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 x1 (*.f64 x1 3)) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3) (*.f64 (-.f64 (+.f64 (*.f64 x1 (*.f64 x1 3)) (*.f64 2 x2)) x1) (*.f64 x1 2)))) (*.f64 (+.f64 (*.f64 (/.f64 (-.f64 (+.f64 (*.f64 x1 (*.f64 x1 3)) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (/.f64 (-.f64 (+.f64 (*.f64 x1 (*.f64 x1 3)) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 16)) -36) (+.f64 (*.f64 x1 x1) (pow.f64 x1 4)))) (*.f64 (+.f64 (*.f64 x1 x1) 1) (+.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 x1 (*.f64 x1 3)) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6)))
101.0ms
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (cbrt.f64 (-.f64 x 1))))
Rules
143783×associate-*r/_binary64
52550×frac-add_binary64
49779×frac-times_binary64
37379×flip-+_binary64
37378×flip3-+_binary64
32262×flip--_binary64
32261×flip3--_binary64
26841×*-un-lft-identity_binary64
26764×times-frac_binary64
24499×add-sqr-sqrt_binary64
23514×cube-div_binary64
16994×add-cube-cbrt_binary64
12804×add-exp-log_binary64
12009×frac-sub_binary64
11066×associate-*l/_binary64
10422×associate-/l/_binary64
8800×add-cbrt-cube_binary64
6258×pow1_binary64
6256×sqrt-prod_binary64
4733×associate-*r*_binary64
4720×prod-exp_binary64
3635×add-log-exp_binary64
3263×associate-*l*_binary64
3195×distribute-lft-out_binary64
3074×div-exp_binary64
2866×associate-/r*_binary64
2801×cbrt-prod_binary64
2758×cbrt-unprod_binary64
2727×difference-of-squares_binary64
2374×sqrt-div_binary64
2046×associate-/l*_binary64
1905×associate-/r/_binary64
1884×unpow-prod-down_binary64
1737×distribute-lft-out--_binary64
1662×cbrt-undiv_binary64
1603×pow-prod-down_binary64
1563×div-inv_binary64
1209×pow-exp_binary64
1091×unswap-sqr_binary64
892×log-prod_binary64
801×sqr-pow_binary64
714×log-pow_binary64
668×pow-to-exp_binary64
666×sqrt-pow1_binary64
621×*-commutative_binary64
598×exp-prod_binary64
584×cube-prod_binary64
498×pow1/2_binary64
465×cbrt-div_binary64
464×clear-num_binary64 frac-2neg_binary64
439×swap-sqr_binary64
437×sub-neg_binary64
433×sum-log_binary64
411×pow-unpow_binary64
333×1-exp_binary64
322×diff-log_binary64
319×rec-exp_binary64
299×pow1/3_binary64
287×rem-sqrt-square_binary64
271×distribute-rgt-in_binary64 distribute-lft-in_binary64
256×difference-of-sqr-1_binary64
233×pow-prod-up_binary64
225×tan-quot_binary64
204×+-commutative_binary64
153×pow-sqr_binary64
149×unpow2_binary64
144×div-sub_binary64
143×pow-pow_binary64
137×log-div_binary64
132×cube-mult_binary64 associate--l+_binary64
116×unpow3_binary64
109×cos-mult_binary64
102×associate-+r+_binary64
97×pow-flip_binary64
95×pow-plus_binary64
94×distribute-rgt-neg-in_binary64
90×rem-log-exp_binary64
82×exp-diff_binary64
76×exp-neg_binary64
75×pow2_binary64
66×associate--r+_binary64
65×neg-sub0_binary64
64×inv-pow_binary64
57×sin-mult_binary64
56×distribute-rgt-out_binary64
55×distribute-lft-neg-in_binary64
52×cosh-undef_binary64
42×rem-cube-cbrt_binary64
40×un-div-inv_binary64
37×rem-exp-log_binary64
35×sqrt-unprod_binary64
33×neg-mul-1_binary64 associate-+l+_binary64
29×associate--l-_binary64
26×distribute-rgt1-in_binary64
23×sub-div_binary64
22×exp-sum_binary64
21×rem-cbrt-cube_binary64 cos-diff_binary64
20×cos-sum_binary64
19×associate--r-_binary64
16×associate-+r-_binary64 asin-acos_binary64 distribute-rgt-out--_binary64
15×sin-diff_binary64 acos-asin_binary64
14×sinh-def_binary64
13×sin-cos-mult_binary64
11×rem-square-sqrt_binary64 distribute-frac-neg_binary64
10×associate-+l-_binary64 sinh-undef_binary64
exp-to-pow_binary64
difference-cubes_binary64 e-exp-1_binary64 unpow-prod-up_binary64 pow-sub_binary64
difference-of-sqr--1_binary64 sin-sum_binary64
sqrt-undiv_binary64 tan-sum_binary64 neg-log_binary64
pow3_binary64 acos-neg_binary64 sqr-sin-a_binary64
sqrt-pow2_binary64 sum-cubes_binary64 cos-2_binary64 sqr-cos-a_binary64 asin-neg_binary64
remove-double-div_binary64 count-2_binary64 tanh-def-a_binary64 tanh-undef_binary64 pow-neg_binary64 distribute-lft1-in_binary64 diff-sin_binary64 tanh-def-b_binary64 mul0-rgt_binary64 unsub-neg_binary64 diff-atan_binary64 tanh-def-c_binary64 diff-cos_binary64

localize9.7s (0.9%)

bsearch6.4s (0.6%)

end4.0ms (0.0%)

Profiling

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