Date:Wednesday, September 16th, 2020
Commit:eff2405d on multiprecision
Hostname:warfa with Racket 7.8
Seed:2020260
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

series1.7min (37.6%)

Calls

439 calls:

3.8s
(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))))))))
3.7s
(sqrt.f64 (*.f64 (*.f64 2 n) (*.f64 U (+.f64 t (*.f64 (/.f64 l Om) (+.f64 (*.f64 l -2) (*.f64 n (*.f64 (/.f64 l Om) (-.f64 U* U)))))))))
3.6s
(sqrt.f64 (*.f64 (*.f64 2 n) (*.f64 U (+.f64 t (*.f64 (/.f64 l Om) (+.f64 (*.f64 l -2) (*.f64 n (*.f64 (/.f64 l Om) (-.f64 U* U)))))))))
3.5s
(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))))))))))
3.5s
(sqrt.f64 (*.f64 (*.f64 2 n) (*.f64 U (+.f64 t (*.f64 (/.f64 l Om) (+.f64 (*.f64 l -2) (*.f64 n (*.f64 (/.f64 l Om) (-.f64 U* U)))))))))

sample1.4min (30.7%)

Algorithm
62×intervals
Results
19.1s34099×body1024valid
15.4s182557×body128valid
6.5s11173×body2048valid
5.5s16112×body512valid
4.6s50043×body128nan
4.4s1272×body4096invalid
2.8s6097×body1024nan
2.8s2996×body4096valid
2.7s24304×body128invalid
2.4s1174×body2048invalid
1.7s7795×body256valid
1.7s4575×body1024invalid
1.0s3172×body512nan
784.0ms1204×body8192valid
682.0ms2541×body512invalid
343.0ms1608×body256nan
329.0ms2355×body128overflowed
271.0ms1452×body256invalid
137.0ms8256×pre128true
5.0ms8×body8192exit
2.0ms3×body2048nan

analyze33.5s (12.3%)

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

prune23.0s (8.5%)

Filtered
17908 candidates to 11303 candidates (36.9%)

simplify13.1s (4.8%)

Algorithm
180×egg-herbie

rewrite7.4s (2.7%)

Algorithm
118×rewrite-expression-head
Calls

439 calls:

142.0ms
(*.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) c0) (sqrt.f64 (/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l)))))
74.0ms
(sqrt.f64 (/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l))))
65.0ms
(/.f64 (/.f64 2 (*.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 k l))) (/.f64 k (/.f64 l (/.f64 1 (cos.f64 k)))))
53.0ms
(+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))
42.0ms
(*.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
Rules
14677×times-frac_binary64
8403×add-sqr-sqrt_binary64
8211×*-un-lft-identity_binary64
7253×add-cube-cbrt_binary64
4559×add-exp-log_binary64
3257×sqrt-prod_binary64
3003×add-cbrt-cube_binary64
1991×cbrt-prod_binary64
1893×prod-exp_binary64
1367×associate-*r*_binary64
1337×pow1_binary64
1188×div-exp_binary64
1157×cbrt-unprod_binary64
800×associate-/r*_binary64
735×unpow-prod-down_binary64
723×div-inv_binary64
687×cbrt-undiv_binary64
675×associate-*l*_binary64
633×associate-*r/_binary64
535×add-log-exp_binary64
463×pow-prod-down_binary64
427×sqrt-div_binary64
390×associate-/l*_binary64
383×associate-/r/_binary64
344×difference-of-squares_binary64
288×pow-exp_binary64
263×frac-times_binary64
261×distribute-lft-out_binary64
243×sqr-pow_binary64
242×associate-*l/_binary64
237×unswap-sqr_binary64
224×flip3-+_binary64 flip-+_binary64
222×exp-prod_binary64
197×distribute-lft-out--_binary64
188×pow-to-exp_binary64
173×flip3--_binary64 flip--_binary64
171×sqrt-pow1_binary64
152×*-commutative_binary64
139×pow-unpow_binary64
102×rem-sqrt-square_binary64
99×clear-num_binary64 frac-2neg_binary64
90×cube-prod_binary64
77×pow1/2_binary64
75×unpow2_binary64
71×cbrt-div_binary64
64×distribute-rgt-in_binary64 distribute-lft-in_binary64
59×tan-quot_binary64
57×associate-/l/_binary64 pow1/3_binary64
54×frac-add_binary64
51×sub-neg_binary64
47×rec-exp_binary64
41×pow-pow_binary64
40×sum-log_binary64
30×log-pow_binary64
23×+-commutative_binary64 pow-prod-up_binary64
18×swap-sqr_binary64
17×pow-flip_binary64 div-sub_binary64 pow-plus_binary64
14×unpow3_binary64 cube-mult_binary64
13×inv-pow_binary64 pow-sqr_binary64
11×difference-of-sqr-1_binary64
10×diff-log_binary64 associate-+r+_binary64
9×cube-div_binary64 pow2_binary64
7×log-prod_binary64 exp-diff_binary64
6×sinh-def_binary64 rem-exp-log_binary64
5×frac-sub_binary64
4×sqrt-undiv_binary64 rem-cube-cbrt_binary64
3×rem-cbrt-cube_binary64 cos-diff_binary64 pow-sub_binary64 cos-sum_binary64 un-div-inv_binary64
2×sqrt-unprod_binary64 acos-asin_binary64 rem-log-exp_binary64 associate-+l+_binary64 distribute-rgt-out_binary64 sinh-undef_binary64 asin-acos_binary64 associate--l+_binary64
1×exp-sum_binary64 pow3_binary64 neg-sub0_binary64 pow-neg_binary64 sub-div_binary64 mul0-rgt_binary64

regimes5.4s (2.0%)

Accuracy

Total 42.0b remaining (22.9%)

Threshold costs 5.3b (2.9%)

8.4b30.7%Toniolo and Linder, Equation (13)
6.5b25.9%Henrywood and Agarwal, Equation (12)
5.8b75.8%Toniolo and Linder, Equation (7)
5.2b0%Maksimov and Kolovsky, Equation (3)
4.6b49.1%Toniolo and Linder, Equation (10+)

localize2.5s (0.9%)

bsearch1.2s (0.4%)

end1.0ms (0.0%)

Profiling

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