Details

analyze435.0ms

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

sample70.0ms

Algorithm

intervals

Results

34.0ms	126×	body	320	valid
21.0ms	126×	body	160	valid
3.0ms	43×	body	80	nan
0.0ms	4×	body	80	valid

simplify289.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (279.0ms)

Iter	Nodes	Cost
0	4835	48
1	4835	48

prune6.0ms

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: 37.9b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
9.0b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
31.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
9×	`sqrt-prod_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
2×	`cbrt-div_binary64` `pow1/2_binary64` `flip3--_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`distribute-lft-out--_binary64` `div-inv_binary64` `associate-*l/_binary64`

Counts

4 → 61

Calls

4 calls:

9.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
8.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
235.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
28.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
29.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify68.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5038	1648

prune160.0ms

Filtered

63 candidates to 73 candidates (-15.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	55	18	73
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	57	18	75

Merged error: 33.7b

Counts

75 → 18

localize18.0ms

Local error

Found 4 expressions with local error:

2.8b	(-.f64 (.f64 g g) (.f64 h h))
7.4b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
31.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

4.0ms	(-.f64 (.f64 g g) (.f64 h h))
9.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(-.f64 (.f64 g g) (.f64 h h))
231.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
29.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify118.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4878	1094
1	4878	1094

prune109.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	16	17
Picked	1	0	1
Done	0	0	0
Total	67	17	84

Merged error: 32.8b

Counts

84 → 17

localize17.0ms

Local error

Found 4 expressions with local error:

2.8b	(-.f64 (.f64 g g) (.f64 h h))
7.4b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
31.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

4.0ms	(-.f64 (.f64 g g) (.f64 h h))
9.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
7.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(-.f64 (.f64 g g) (.f64 h h))
229.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
30.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify112.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4878	1094
1	4878	1094

prune102.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	67	16	83

Merged error: 32.7b

Counts

83 → 16

localize26.0ms

Local error

Found 4 expressions with local error:

31.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.8b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_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` `difference-of-squares_binary64` `flip--_binary64`

Counts

4 → 64

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
29.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
32.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify126.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4814	1068
1	4814	1068

prune103.0ms

Filtered

64 candidates to 76 candidates (-18.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	15	15
Picked	1	0	1
Done	0	0	0
Total	76	16	92

Merged error: 32.7b

Counts

92 → 16

regimes171.0ms

Accuracy

79.1% (1.0b remaining)

Error of 31.6b against oracle of 30.7b and baseline of 35.4b

bsearch85.0ms

Steps

Iters	Range		Point
9	4.0021692540469987e-172	6.2131150356221834e-164	6.120718425137781e-164

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	75	97
1	75	97

end0.0ms

sample2.0s

Algorithm

intervals

Results

956.0ms	3714×	body	320	valid
710.0ms	4137×	body	160	valid
99.0ms	1182×	body	80	nan
13.0ms	149×	body	80	valid

Details

analyze435.0ms

sample70.0ms

simplify289.0ms

prune6.0ms

localize20.0ms

rewrite27.0ms

series532.0ms

simplify68.0ms

prune160.0ms

localize18.0ms

rewrite24.0ms

series317.0ms

simplify118.0ms

prune109.0ms

localize17.0ms

rewrite26.0ms

series315.0ms

simplify112.0ms

prune102.0ms

localize26.0ms

rewrite20.0ms

series116.0ms

simplify126.0ms

prune103.0ms

regimes171.0ms

bsearch85.0ms

simplify4.0ms

end0.0ms

sample2.0s

Profiling