Details

Time bar (total: 4.2s)

analyze977.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%74.9%0.1%6
25%74.9%0.1%7
37.4%62.4%0.1%8
37.4%62.4%0.1%9
37.4%62.4%0.1%10
43.7%56.2%0.1%11
43.7%56.2%0.1%12
43.7%56.2%0.1%13
61.7%38.2%0.1%14

sample30.0ms

Algorithm
intervals
Results
21.0ms256×body80valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (15.0ms)

IterNodesCost
0512137

prune10.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 25.7b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x)
0.1b
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
0.1b
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
25.0b
(/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
15×add-exp-log_binary64 add-cbrt-cube_binary64
12×*-un-lft-identity_binary64 add-cube-cbrt_binary64
10×pow1_binary64
associate-*r*_binary64 associate-*l*_binary64
associate-/l/_binary64 associate-*l/_binary64
flip3-+_binary64 flip-+_binary64
add-log-exp_binary64 cbrt-unprod_binary64 prod-exp_binary64 frac-times_binary64
pow-prod-down_binary64 associate-/r*_binary64 flip3--_binary64 unswap-sqr_binary64 times-frac_binary64 flip--_binary64 *-commutative_binary64
cbrt-undiv_binary64 associate-*r/_binary64 associate-/r/_binary64 div-exp_binary64
clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64
Counts
4 → 91
Calls
4 calls:
15.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x)
12.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
8.0ms
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
35.0ms
(/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))

series68.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x)
4.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
7.0ms
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
47.0ms
(/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))

simplify62.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049502195
149502195

prune195.0ms

Filtered
83 candidates to 103 candidates (-24.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New958103
Fresh000
Picked101
Done000
Total968104

Merged error: 0.0b

Counts
104 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y))
0.1b
(*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
0.1b
(*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
22.7b
(/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64 add-cube-cbrt_binary64
12×add-exp-log_binary64 add-cbrt-cube_binary64
10×pow1_binary64
associate-*r*_binary64 associate-*l*_binary64 times-frac_binary64
associate-*r/_binary64
flip3-+_binary64 flip-+_binary64
add-log-exp_binary64
pow-prod-down_binary64 associate-/r*_binary64 cbrt-unprod_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 prod-exp_binary64 associate-/l*_binary64 *-commutative_binary64
associate-/l/_binary64 associate-/r/_binary64
cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
4 → 97
Calls
4 calls:
15.0ms
(*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y))
12.0ms
(*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
8.0ms
(*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
30.0ms
(/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))

series63.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y))
4.0ms
(*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
6.0ms
(*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
42.0ms
(/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))

simplify72.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049472422
149472422

prune157.0ms

Filtered
78 candidates to 109 candidates (-39.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1063109
Fresh257
Picked101
Done000
Total1098117

Merged error: 0.0b

Counts
117 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

7.0b
(sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
7.0b
(sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
15.5b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))) (/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))))
19.5b
(/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt_binary64
76×times-frac_binary64
53×*-un-lft-identity_binary64
47×add-cube-cbrt_binary64 sqrt-prod_binary64
28×add-exp-log_binary64
24×associate-*r*_binary64 associate-*l*_binary64
18×add-cbrt-cube_binary64
15×unswap-sqr_binary64
10×sqrt-div_binary64
div-exp_binary64
pow1_binary64 prod-exp_binary64
flip3-+_binary64 associate-/r*_binary64 associate-/r/_binary64 flip-+_binary64
cbrt-undiv_binary64
add-log-exp_binary64 cbrt-unprod_binary64
associate-/l*_binary64 div-inv_binary64
associate-/l/_binary64 pow1/2_binary64 1-exp_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 rec-exp_binary64
pow-prod-down_binary64 associate-*r/_binary64 clear-num_binary64 frac-2neg_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 160
Calls
4 calls:
14.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
14.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
58.0ms
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))) (/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))))
36.0ms
(/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))

series115.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
7.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
43.0ms
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))) (/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))))
58.0ms
(/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))

simplify107.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049547419
149547419

prune353.0ms

Filtered
111 candidates to 172 candidates (-55.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1720172
Fresh077
Picked011
Done000
Total1728180

Merged error: 0.0b

Counts
180 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
0.1b
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
0.1b
(/.f64 1 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
25.2b
(*.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (/.f64 1 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log_binary64
27×add-sqr-sqrt_binary64
23×*-un-lft-identity_binary64 add-cube-cbrt_binary64
22×add-cbrt-cube_binary64
21×associate-*r*_binary64
18×times-frac_binary64
16×frac-times_binary64 associate-*l/_binary64
14×pow1_binary64 prod-exp_binary64
10×flip3-+_binary64 flip-+_binary64
cbrt-unprod_binary64
associate-*l*_binary64
flip3--_binary64 div-exp_binary64 flip--_binary64
pow-prod-down_binary64 associate-*r/_binary64
add-log-exp_binary64 associate-/r/_binary64
associate-/r*_binary64 1-exp_binary64 cbrt-undiv_binary64 rec-exp_binary64 associate-/l*_binary64 *-commutative_binary64
unswap-sqr_binary64 div-inv_binary64
clear-num_binary64 inv-pow_binary64 frac-2neg_binary64 un-div-inv_binary64 pow-flip_binary64
Counts
4 → 129
Calls
4 calls:
12.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
8.0ms
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
17.0ms
(/.f64 1 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
40.0ms
(*.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (/.f64 1 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))

series62.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
7.0ms
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
6.0ms
(/.f64 1 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
44.0ms
(*.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (/.f64 1 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))

simplify95.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049473749
149473749

prune199.0ms

Filtered
98 candidates to 141 candidates (-43.9%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1383141
Fresh516
Picked011
Done011
Total1436149

Merged error: 0b

Counts
149 → 6

regimes241.0ms

Accuracy

97.8% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 24.9b

bsearch47.0ms

Steps
ItersRangePoint
8
2.969496166456181e+27
8.069591365570183e+31
7.952413405146993e+31
10
-1.237267499670971e+53
-3.0780565054624913e+41
-1.0950106885243919e+51

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08263
18263

end0.0ms

sample836.0ms

Algorithm
intervals
Results
656.0ms8000×body80valid
0.0msbody80invalid

Profiling

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