Details

analyze546.0ms

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

sample39.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
2.0ms	22×	body	80	nan
1.0ms	14×	body	80	invalid

simplify698.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (268.0ms)

Iter	Nodes	Cost
0	2747	36
1	2747	36

prune11.0ms

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: 17.5b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
2.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite45.0ms

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 a)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
21.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
28.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify34.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5018	911

prune107.0ms

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: 4.2b

Counts

68 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

5.5b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

3.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify31.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5631	898

prune111.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	67	7	74

Merged error: 4.2b

Counts

74 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

14.2b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `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`
1×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64`

Counts

4 → 57

Calls

4 calls:

17.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify47.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5116	926

prune102.0ms

Filtered

58 candidates to 69 candidates (-19.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	69	7	76

Merged error: 4.2b

Counts

76 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 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:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series67.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4927	924
1	4927	924

prune142.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	72	7	79

Merged error: 4.2b

Counts

79 → 7

regimes214.0ms

Accuracy

93% (0.9b remaining)

Error of 8.5b against oracle of 7.7b and baseline of 20.0b

bsearch58.0ms

Steps

Iters	Range		Point
6	4.36525861707894e+104	3.670797843390954e+105	1.1407010824252603e+105
10	-2.2371059558318353e+164	-6.357254606738086e+153	-1.3526827374990375e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	123	123
1	123	123

end0.0ms

sample1.0s

Algorithm

intervals

Results

704.0ms	8000×	body	80	valid
53.0ms	656×	body	80	nan
33.0ms	399×	body	80	invalid

Details

analyze546.0ms

sample39.0ms

simplify698.0ms

prune11.0ms

localize23.0ms

rewrite45.0ms

series70.0ms

simplify34.0ms

prune107.0ms

localize23.0ms

rewrite19.0ms

series66.0ms

simplify31.0ms

prune111.0ms

localize23.0ms

rewrite33.0ms

series66.0ms

simplify47.0ms

prune102.0ms

localize31.0ms

rewrite21.0ms

series67.0ms

simplify37.0ms

prune142.0ms

regimes214.0ms

bsearch58.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling