Details

analyze784.0ms

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

sample69.0ms

Algorithm

intervals

Results

12.0ms	163×	body	80	valid
11.0ms	31×	body	640	valid
10.0ms	30×	body	1280	valid
7.0ms	27×	body	640	nan
6.0ms	17×	body	1280	nan
4.0ms	22×	body	320	valid
3.0ms	40×	body	80	nan
2.0ms	12×	body	320	nan
1.0ms	10×	body	160	valid
1.0ms	4×	body	160	nan

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5225	27

prune3.0ms

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: 44.7b

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)
12.8b	(-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (*.f64 l l))
21.1b	(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)))

rewrite56.0ms

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:

19.0ms	(/.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)
15.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (*.f64 l l))
15.0ms	(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)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/.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)
63.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) (+.f64 (.f64 l l) (.f64 2.0 (.f64 t t)))) (*.f64 l l))
209.0ms	(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)))

simplify48.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4979	1997
1	4979	1997

prune145.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	4	92

Merged error: 4.8b

Counts

92 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

4.4b	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
7.2b	(/.f64 (*.f64 l l) x)
8.6b	(/.f64 (*.f64 t t) x)
26.8b	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite29.0ms

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)))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.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)
30.0ms	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4973	1345
1	4973	1345

prune120.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	80	10	90

Merged error: 3.0b

Counts

90 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2.0) t)
4.4b	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
8.6b	(/.f64 (*.f64 t t) x)
26.8b	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite31.0ms

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 x l)))))
7.0ms	(/.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 x l))))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 (sqrt.f64 2.0) t)
17.0ms	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
4.0ms	(/.f64 (*.f64 t t) x)
30.0ms	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4985	1327
1	4985	1327

prune115.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	87	10	97

Merged error: 2.9b

Counts

97 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2.0)) (cbrt.f64 (sqrt.f64 2.0))) (*.f64 t (cbrt.f64 (sqrt.f64 2.0))))
4.4b	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
8.6b	(/.f64 (*.f64 t t) x)
26.8b	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64`
17×	`pow1_binary64`
15×	`add-cbrt-cube_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`pow-prod-down_binary64` `associate-*r/_binary64` `add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`flip3-+_binary64` `frac-add_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64` `associate-+r+_binary64`
1×	`pow1/2_binary64` `associate-r_binary64` `distribute-lft-in_binary64` `associate-l_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:

11.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2.0)) (cbrt.f64 (sqrt.f64 2.0))) (*.f64 t (cbrt.f64 (sqrt.f64 2.0))))
9.0ms	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
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 x l))))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2.0)) (cbrt.f64 (sqrt.f64 2.0))) (*.f64 t (cbrt.f64 (sqrt.f64 2.0))))
18.0ms	(+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
4.0ms	(/.f64 (*.f64 t t) x)
32.0ms	(sqrt.f64 (+.f64 (.f64 4.0 (/.f64 (.f64 t t) x)) (.f64 2.0 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4965	1323
1	4965	1323

prune91.0ms

Filtered

58 candidates to 87 candidates (-50.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	86	11	97

Merged error: 2.9b

Counts

97 → 11

regimes608.0ms

Accuracy

76.9% (5.6b remaining)

Error of 9.8b against oracle of 4.2b and baseline of 28.2b

bsearch418.0ms

Steps

Iters	Range		Point
10	3.730194580565081e+41	4.698640247924842e+54	4.633595256269455e+54
8	9.472984164457177e-165	4.863465518416841e-160	9.737845307435373e-165
10	1.0554483519623456e-221	3.309682420602759e-204	3.219152109280772e-204
10	-2.135230378654967e+63	-9.97479881903036e+45	-2.0889904105457687e+63

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	127	116
1	127	116

end0.0ms

sample1.9s

Algorithm

intervals

Results

375.0ms	5156×	body	80	valid
286.0ms	839×	body	1280	valid
276.0ms	1029×	body	640	valid
216.0ms	639×	body	1280	nan
161.0ms	613×	body	640	nan
123.0ms	608×	body	320	valid
94.0ms	1396×	body	80	nan
68.0ms	340×	body	320	nan
50.0ms	368×	body	160	valid
22.0ms	166×	body	160	nan

Details

analyze784.0ms

sample69.0ms

simplify42.0ms

prune3.0ms

localize16.0ms

rewrite56.0ms

series417.0ms

simplify48.0ms

prune145.0ms

localize15.0ms

rewrite29.0ms

series59.0ms

simplify45.0ms

prune120.0ms

localize15.0ms

rewrite31.0ms

series56.0ms

simplify45.0ms

prune115.0ms

localize18.0ms

rewrite36.0ms

series59.0ms

simplify47.0ms

prune91.0ms

regimes608.0ms

bsearch418.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling