Details

analyze554.0ms

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
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample43.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
1.0ms	17×	body	80	nan
1.0ms	13×	body	80	invalid

simplify683.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (262.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune12.0ms

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: 19.0b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_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` `difference-of-squares_binary64`
1×	`distribute-lft-out--_binary64`

Counts

4 → 55

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
23.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
28.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify52.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4994	921
1	4994	921

prune131.0ms

Filtered

53 candidates to 67 candidates (-26.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	61	6	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	6	68

Merged error: 7.0b

Counts

68 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
10×	`sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`difference-of-squares_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `distribute-lft-out--_binary64`

Counts

4 → 59

Calls

4 calls:

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

series74.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify43.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4974	975
1	4974	975

prune134.0ms

Filtered

58 candidates to 71 candidates (-22.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 7.0b

Counts

77 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify50.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4979	932
1	4979	932

prune145.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 7.0b

Counts

78 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series72.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify49.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4979	932
1	4979	932

prune143.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	72	6	78

Merged error: 7.0b

Counts

78 → 6

regimes236.0ms

Accuracy

90.5% (1.2b remaining)

Error of 8.6b against oracle of 7.4b and baseline of 19.8b

bsearch57.0ms

Steps

Iters	Range		Point
9	4.978070574921307e+116	5.588961238148798e+121	6.490997278865284e+120
8	-1.0112877333575733e+66	-2.4780880203930075e+62	-9.12593955228803e+65

simplify12.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	559	131
1	559	131

end0.0ms

sample1.0s

Algorithm

intervals

Results

705.0ms	8000×	body	80	valid
57.0ms	680×	body	80	nan
33.0ms	394×	body	80	invalid

Details

analyze554.0ms

sample43.0ms

simplify683.0ms

prune12.0ms

localize22.0ms

rewrite43.0ms

series75.0ms

simplify52.0ms

prune131.0ms

localize23.0ms

rewrite24.0ms

series74.0ms

simplify43.0ms

prune134.0ms

localize24.0ms

rewrite21.0ms

series71.0ms

simplify50.0ms

prune145.0ms

localize25.0ms

rewrite20.0ms

series72.0ms

simplify49.0ms

prune143.0ms

regimes236.0ms

bsearch57.0ms

simplify12.0ms

end0.0ms

sample1.0s

Profiling