Details

analyze408.0ms

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

sample64.0ms

Algorithm

intervals

Results

29.0ms	117×	body	320	valid
21.0ms	135×	body	160	valid
3.0ms	37×	body	80	nan
0.0ms	4×	body	80	valid

simplify102.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4881	36
1	4881	36

prune12.0ms

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: 36.4b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

6.2b	(cbrt (* 1.0 (/ (- (neg g) (sqrt (- (* g g) (* h h)))) (* 2.0 a))))
7.8b	(cbrt (* 1.0 (/ (- (sqrt (- (* g g) (* h h))) g) (* 2.0 a))))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite33.0ms

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:

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

series121.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(cbrt (* 1.0 (/ (- (neg g) (sqrt (- (* g g) (* h h)))) (* 2.0 a))))
52.0ms	(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)))

simplify33.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5187	863

prune218.0ms

Filtered

56 candidates to 64 candidates (-14.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	49	15	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	51	15	66

Merged error: 32.7b

Counts

66 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
6.2b	(cbrt (* 1.0 (/ (- (neg g) (sqrt (- (* g g) (* h h)))) (* 2.0 a))))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite26.0ms

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))
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)))

series74.0ms

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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4991	750
1	4991	750

prune211.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	64	17	81

Merged error: 31.8b

Counts

81 → 17

localize19.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
7.8b	(cbrt (* 1.0 (/ (- (sqrt (- (* g g) (* h h))) g) (* 2.0 a))))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
54.0ms	(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)))

simplify74.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5251	737

prune198.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	3	13	16
Picked	0	1	1
Done	0	0	0
Total	67	16	83

Merged error: 31.8b

Counts

83 → 16

localize29.0ms

Local error

Found 4 expressions with local error:

31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series27.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify66.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4827	700
1	4827	700

prune233.0ms

Filtered

64 candidates to 76 candidates (-18.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	75	17	92

Merged error: 31.7b

Counts

92 → 17

regimes623.0ms

Accuracy

73.9% (0.8b remaining)

Error of 31.5b against oracle of 30.7b and baseline of 33.9b

bsearch82.0ms

Steps

Iters	Range		Point
9	1.7771280949230838e-212	4.225660128622964e-206	4.174071724439994e-206

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	132	72
1	132	72

end0.0ms

sample1.8s

Algorithm

intervals

Results

874.0ms	3728×	body	320	valid
653.0ms	4122×	body	160	valid
95.0ms	1208×	body	80	nan
12.0ms	150×	body	80	valid

Details

analyze408.0ms

sample64.0ms

simplify102.0ms

prune12.0ms

localize18.0ms

rewrite33.0ms

series121.0ms

simplify33.0ms

prune218.0ms

localize22.0ms

rewrite26.0ms

series74.0ms

simplify46.0ms

prune211.0ms

localize19.0ms

rewrite23.0ms

series73.0ms

simplify74.0ms

prune198.0ms

localize29.0ms

rewrite18.0ms

series27.0ms

simplify66.0ms

prune233.0ms

regimes623.0ms

bsearch82.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling