Details

analyze443.0ms

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%	68.6%	18.9%	6
18.7%	62.4%	18.9%	7
18.7%	59.3%	22%	8
28.1%	39%	32.9%	9
32.8%	34.3%	32.9%	10
32.8%	32%	35.3%	11
38.2%	20.7%	41.1%	12
41%	17.9%	41.1%	13
41%	16.6%	42.5%	14

sample73.0ms

Algorithm

intervals

Results

32.0ms	124×	body	320	valid
22.0ms	126×	body	160	valid
3.0ms	39×	body	80	nan
1.0ms	6×	body	80	valid

simplify109.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4901	36
1	4901	36

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 36.2b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

7.5b	(cbrt (* 1.0 (/ (- (sqrt (- (* g g) (* h h))) g) (* 2.0 a))))
9.3b	(cbrt (* 1.0 (/ (- (neg g) (sqrt (- (* g g) (* h h)))) (* 2.0 a))))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(sqrt (- (* g g) (* h h)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `cbrt-div` `flip3--` `sqrt-pow1` `pow1/2` `pow1/3` `associate-*r/` `flip--` `difference-of-squares`

Counts

4 → 52

Calls

4 calls:

9.0ms	(cbrt (* 1.0 (/ (- (sqrt (- (* g g) (* h h))) g) (* 2.0 a))))
12.0ms	(cbrt (* 1.0 (/ (- (neg g) (sqrt (- (* g g) (* h h)))) (* 2.0 a))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(cbrt (* 1.0 (/ (- (sqrt (- (* g g) (* h h))) g) (* 2.0 a))))
55.0ms	(cbrt (* 1.0 (/ (- (neg g) (sqrt (- (* g g) (* h h)))) (* 2.0 a))))
9.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify42.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5107	883

prune252.0ms

Filtered

56 candidates to 64 candidates (-14.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	47	17	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	49	17	66

Merged error: 32.2b

Counts

66 → 17

localize23.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
7.5b	(cbrt (* 1.0 (/ (- (sqrt (- (* g g) (* h h))) g) (* 2.0 a))))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(sqrt (- (* g g) (* h h)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-prod` `sub-neg` `cbrt-div` `pow1/3` `diff-log` `associate-*r/`

Counts

4 → 54

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
10.0ms	(cbrt (* 1.0 (/ (- (sqrt (- (* g g) (* h h))) g) (* 2.0 a))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
57.0ms	(cbrt (* 1.0 (/ (- (sqrt (- (* g g) (* h h))) g) (* 2.0 a))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify36.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5142	741

prune246.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	64	19	83

Merged error: 31.6b

Counts

83 → 19

localize21.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
9.3b	(cbrt (* 1.0 (/ (- (neg g) (sqrt (- (* g g) (* h h)))) (* 2.0 a))))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(sqrt (- (* g g) (* h h)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-prod` `sub-neg` `cbrt-div` `pow1/3` `diff-log` `associate-*r/`

Counts

4 → 54

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
14.0ms	(cbrt (* 1.0 (/ (- (neg g) (sqrt (- (* g g) (* h h)))) (* 2.0 a))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
55.0ms	(cbrt (* 1.0 (/ (- (neg g) (sqrt (- (* g g) (* h h)))) (* 2.0 a))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify39.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5014	754

prune229.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	7	11	18
Picked	1	0	1
Done	0	0	0
Total	69	16	85

Merged error: 31.5b

Counts

85 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

16.6b	(- (* (sqrt (sqrt (- (* g g) (* h h)))) (sqrt (sqrt (- (* g g) (* h h))))) g)
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(sqrt (- (* g g) (* h h)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
11×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `difference-of-squares`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 60

Calls

4 calls:

15.0ms	(- (* (sqrt (sqrt (- (* g g) (* h h)))) (sqrt (sqrt (- (* g g) (* h h))))) g)
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* (sqrt (sqrt (- (* g g) (* h h)))) (sqrt (sqrt (- (* g g) (* h h))))) g)
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify60.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4878	708
1	4878	708

prune146.0ms

Filtered

62 candidates to 72 candidates (-16.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	72	16	88

Merged error: 31.0b

Counts

88 → 16

regimes714.0ms

Accuracy

85.7% (1.3b remaining)

Error of 31.3b against oracle of 30.1b and baseline of 38.9b

bsearch98.0ms

Steps

Iters	Range		Point
11	-2.973142410690192e-173	-2.462573784346457e-197	-2.9415560676817554e-173

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	230	92
1	230	92

end0.0ms

sample2.1s

Algorithm

intervals

Results

989.0ms	3801×	body	320	valid
726.0ms	4079×	body	160	valid
113.0ms	1334×	body	80	nan
11.0ms	120×	body	80	valid

Details

analyze443.0ms

sample73.0ms

simplify109.0ms

prune14.0ms

localize19.0ms

rewrite30.0ms

series126.0ms

simplify42.0ms

prune252.0ms

localize23.0ms

rewrite23.0ms

series77.0ms

simplify36.0ms

prune246.0ms

localize21.0ms

rewrite27.0ms

series75.0ms

simplify39.0ms

prune229.0ms

localize25.0ms

rewrite29.0ms

series30.0ms

simplify60.0ms

prune146.0ms

regimes714.0ms

bsearch98.0ms

simplify3.0ms

end0.0ms

sample2.1s

Profiling