Details

analyze466.0ms

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample40.0ms

Algorithm

intervals

Results

9.0ms	180×	body	80	valid
8.0ms	33×	body	1280	valid
6.0ms	20×	body	2560	valid
2.0ms	13×	body	640	valid
1.0ms	25×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	17×	body	80	invalid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify207.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (204.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 29.3b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3.0 a) c)
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
6×	`add-cube-cbrt_binary64`
4×	`sqrt-prod_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(.f64 (.f64 3.0 a) c)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (.f64 3.0 a) c)
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
7.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4915	799
1	4915	799

prune103.0ms

Filtered

51 candidates to 70 candidates (-37.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	10	71

Merged error: 10.3b

Counts

71 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
18.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 52

Calls

4 calls:

4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
7.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5017	808

prune98.0ms

Filtered

52 candidates to 64 candidates (-23.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	64	10	74

Merged error: 10.3b

Counts

74 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
8.1b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))) b)
19.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
19.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
4×	`cbrt-div_binary64` `pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `pow1/3_binary64`

Counts

4 → 48

Calls

4 calls:

4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
9.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))) b)
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
39.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))) b)
22.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
24.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify34.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5144	1069

prune111.0ms

Filtered

54 candidates to 60 candidates (-11.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	58	12	70

Merged error: 10.3b

Counts

70 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

19.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
19.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
19.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
19.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`cbrt-div_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `pow1/3_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
23.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
23.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))
23.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5240	948

prune128.0ms

Filtered

60 candidates to 64 candidates (-6.7%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	64	12	76

Merged error: 10.3b

Counts

76 → 12

regimes410.0ms

Accuracy

95.4% (1.0b remaining)

Error of 13.0b against oracle of 12.0b and baseline of 34.2b

bsearch93.0ms

Steps

Iters	Range	Point
8	3.388583924634284e+105	9.139550096422047e+108	3.4989832974040957e+108
9	2.053163735367116e-113	1.5168780676120168e-108	2.0737225518150114e-113
8	-5.472905454030852e+156	-8.6739741544534e+151	-1.3217401295489042e+154

Iters

Range

Point

3.388583924634284e+105

9.139550096422047e+108

3.4989832974040957e+108

2.053163735367116e-113

1.5168780676120168e-108

2.0737225518150114e-113

-5.472905454030852e+156

-8.6739741544534e+151

-1.3217401295489042e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	144	78
1	144	78

end0.0ms

sample1.2s

Algorithm

intervals

Results

318.0ms	1064×	body	2560	valid
274.0ms	5180×	body	80	valid
213.0ms	870×	body	1280	valid
89.0ms	452×	body	640	valid
45.0ms	126×	body	5120	valid
33.0ms	643×	body	80	nan
33.0ms	219×	body	320	valid
22.0ms	384×	body	80	invalid
9.0ms	89×	body	160	valid

Details

analyze466.0ms

sample40.0ms

simplify207.0ms

prune7.0ms

localize12.0ms

rewrite23.0ms

series41.0ms

simplify45.0ms

prune103.0ms

localize14.0ms

rewrite19.0ms

series46.0ms

simplify41.0ms

prune98.0ms

localize13.0ms

rewrite23.0ms

series93.0ms

simplify34.0ms

prune111.0ms

localize21.0ms

rewrite19.0ms

series94.0ms

simplify70.0ms

prune128.0ms

regimes410.0ms

bsearch93.0ms

simplify3.0ms

end0.0ms

sample1.2s

Profiling