Details

analyze780.0ms

Algorithm

Search

True	Other	False	Iter
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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

sample68.0ms

Algorithm

intervals

Results

12.0ms	166×	body	80	valid
11.0ms	23×	body	1280	valid
9.0ms	37×	body	640	valid
7.0ms	22×	body	1280	nan
5.0ms	22×	body	640	nan
4.0ms	19×	body	320	valid
4.0ms	56×	body	80	nan
2.0ms	12×	body	320	nan
1.0ms	11×	body	160	valid
1.0ms	4×	body	160	nan

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5225	27

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 44.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2.0) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2.0) t)
13.0b	(-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (*.f64 l l))
21.5b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (*.f64 l l)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

21.0ms	(/.f64 (.f64 (sqrt.f64 2.0) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (.f64 l l))))
5.0ms	(*.f64 (sqrt.f64 2.0) t)
14.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (*.f64 l l))
14.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (*.f64 l l)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/.f64 (.f64 (sqrt.f64 2.0) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (.f64 l l))))
5.0ms	(*.f64 (sqrt.f64 2.0) t)
72.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (*.f64 l l))
260.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (*.f64 l l)))

simplify47.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5044	2021

prune162.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	85	6	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 6.4b

Counts

92 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.9b	(/.f64 (*.f64 l l) x)
8.6b	(/.f64 (*.f64 t t) x)
29.0b	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `times-frac_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`sqrt-prod_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `associate-+r+_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)
8.0ms	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
4.0ms	(/.f64 (*.f64 l l) x)
4.0ms	(/.f64 (*.f64 t t) x)
33.0ms	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4973	1345
1	4973	1345

prune128.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	81	11	92

Merged error: 4.0b

Counts

92 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2.0) t)
3.8b	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
8.6b	(/.f64 (*.f64 t t) x)
29.0b	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`flip3-+_binary64` `frac-add_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`associate-/r_binary64` `associate-r*_binary64` `times-frac_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

5.0ms	(*.f64 (sqrt.f64 2.0) t)
9.0ms	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
5.0ms	(/.f64 (*.f64 t t) x)
8.0ms	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 (sqrt.f64 2.0) t)
18.0ms	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
4.0ms	(/.f64 (*.f64 t t) x)
34.0ms	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

simplify28.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5058	1337

prune121.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	87	11	98

Merged error: 4.0b

Counts

98 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
3.8b	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
8.6b	(/.f64 (*.f64 t t) x)
29.0b	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`pow1_binary64`
11×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`associate-*r/_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `pow1/3_binary64` `associate-l_binary64`
4×	`flip3-+_binary64` `frac-add_binary64` `unswap-sqr_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `pow-sqr_binary64` `associate-+r+_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
9.0ms	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
5.0ms	(/.f64 (*.f64 t t) x)
9.0ms	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
22.0ms	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
7.0ms	(/.f64 (*.f64 t t) x)
36.0ms	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4977	1653
1	4977	1653

prune114.0ms

Filtered

78 candidates to 105 candidates (-34.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	105	11	116

Merged error: 4.0b

Counts

116 → 11

regimes589.0ms

Accuracy

76.4% (5.6b remaining)

Error of 9.3b against oracle of 3.7b and baseline of 27.5b

bsearch459.0ms

Steps

Iters	Range		Point
5	5.755926755557875e+106	1.6559792646790436e+107	1.400943711969558e+107
8	1.4474758852172723e-170	1.3099153101412675e-167	1.4633199475026642e-170
8	4.031360803645653e-277	1.7202346864725826e-273	1.6984376092331043e-273
5	-1.6375116051793367e-280	-7.230139701499095e-281	-1.6173039977917613e-280
5	-4.3996886225171295e-246	-1.603266749035457e-246	-1.6304660526178e-246
7	-2.2376876751237564e+75	-5.873251286343534e+73	-2.0540059517808046e+75

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	161	215
1	161	215

end0.0ms

sample1.9s

Algorithm

intervals

Results

362.0ms	5140×	body	80	valid
284.0ms	871×	body	1280	valid
266.0ms	994×	body	640	valid
186.0ms	561×	body	1280	nan
153.0ms	595×	body	640	nan
129.0ms	651×	body	320	valid
96.0ms	1421×	body	80	nan
62.0ms	325×	body	320	nan
47.0ms	344×	body	160	valid
23.0ms	179×	body	160	nan

Details

analyze780.0ms

sample68.0ms

simplify41.0ms

prune4.0ms

localize16.0ms

rewrite57.0ms

series462.0ms

simplify47.0ms

prune162.0ms

localize17.0ms

rewrite30.0ms

series60.0ms

simplify50.0ms

prune128.0ms

localize15.0ms

rewrite30.0ms

series62.0ms

simplify28.0ms

prune121.0ms

localize19.0ms

rewrite32.0ms

series89.0ms

simplify49.0ms

prune114.0ms

regimes589.0ms

bsearch459.0ms

simplify4.0ms

end0.0ms

sample1.9s

Profiling