Details

sample68.0ms

Algorithm

intervals

Results

19.0ms	45×	body	1280	valid
16.0ms	18×	body	2560	valid
8.0ms	129×	body	80	valid
7.0ms	28×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	13×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	11	7
1	13	7
2	13	7

prune3.0ms

Filtered

1 candidates to 0 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: 36.6b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

7.9b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
28.8b	(sin (/ x (* y 2.0)))
29.3b	(tan (/ x (* y 2.0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`tan-quot`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `associate-/l/`

Counts

3 → 49

Calls

3 calls:

23.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
7.0ms	(sin (/ x (* y 2.0)))
7.0ms	(tan (/ x (* y 2.0)))

series100.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
10.0ms	(sin (/ x (* y 2.0)))
43.0ms	(tan (/ x (* y 2.0)))

simplify98.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	144	485
1	414	441
2	1658	441
3	5001	441

prune170.0ms

Filtered

58 candidates to 50 candidates (86.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	45	13	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	13	59

Merged error: 26.6b

Counts

59 → 13

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify4.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune35.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	12	12
Picked	1	1
Done	0	0
Total	13	13

Merged error: 26.6b

Counts

13 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(log1p (expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))))
7.9b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
28.8b	(sin (/ x (* y 2.0)))
29.3b	(tan (/ x (* y 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`pow1` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`tan-quot` `log1p-expm1`
1×	`cbrt-undiv` `log1p-udef` `frac-2neg` `div-exp` `clear-num` `div-inv` `associate-/l/`

Counts

4 → 61

Calls

4 calls:

1.0ms	(log1p (expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))))
16.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
8.0ms	(sin (/ x (* y 2.0)))
8.0ms	(tan (/ x (* y 2.0)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(log1p (expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))))
42.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
10.0ms	(sin (/ x (* y 2.0)))
48.0ms	(tan (/ x (* y 2.0)))

simplify105.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	157	598
1	431	539
2	1677	539
3	5002	539

prune205.0ms

Filtered

73 candidates to 59 candidates (80.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	7	4	11
Picked	1	0	1
Done	0	1	1
Total	75	11	86

Merged error: 26.6b

Counts

86 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

28.8b	(sin (/ x (* y 2.0)))
29.3b	(tan (/ x (* y 2.0)))
29.3b	(tan (/ x (* y 2.0)))
29.3b	(tan (/ x (* y 2.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot`

Counts

4 → 39

Calls

4 calls:

8.0ms	(sin (/ x (* y 2.0)))
8.0ms	(tan (/ x (* y 2.0)))
8.0ms	(tan (/ x (* y 2.0)))
8.0ms	(tan (/ x (* y 2.0)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sin (/ x (* y 2.0)))
48.0ms	(tan (/ x (* y 2.0)))
43.0ms	(tan (/ x (* y 2.0)))
50.0ms	(tan (/ x (* y 2.0)))

simplify91.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	59	250
1	115	222
2	367	222
3	1731	222
4	5001	222

prune195.0ms

Filtered

51 candidates to 47 candidates (92.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	50	12	62

Merged error: 26.5b

Counts

62 → 12

regimes294.0ms

Accuracy

36% (1.6b remaining)

Error of 27.9b against oracle of 26.3b and baseline of 28.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	35
1	19	35

end0.0ms

sample2.1s

Algorithm

intervals

Results

618.0ms	1377×	body	1280	valid
562.0ms	611×	body	2560	valid
298.0ms	1074×	body	640	valid
241.0ms	4071×	body	80	valid
121.0ms	563×	body	320	valid
46.0ms	304×	body	160	valid