Details

sample95.0ms

Algorithm

intervals

Results

31.0ms	26×	body	2560	valid
23.0ms	40×	body	1280	valid
11.0ms	29×	body	640	valid
10.0ms	138×	body	80	valid
3.0ms	13×	body	320	valid
2.0ms	10×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune5.0ms

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: 33.0b

Counts

2 → 1

localize26.0ms

Local error

Found 3 expressions with local error:

6.0b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
26.9b	(sin (/ x (* y 2.0)))
26.9b	(tan (/ x (* y 2.0)))

rewrite12.0ms

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:

6.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
2.0ms	(sin (/ x (* y 2.0)))
2.0ms	(tan (/ x (* y 2.0)))

series96.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
9.0ms	(sin (/ x (* y 2.0)))
41.0ms	(tan (/ x (* y 2.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	146	485
1	433	441
2	1789	441
3	5001	441

prune205.0ms

Filtered

58 candidates to 50 candidates (86.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	44	14	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	14	59

Merged error: 24.9b

Counts

59 → 14

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

prune34.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	13	13
Picked	1	1
Done	0	0
Total	14	14

Merged error: 24.9b

Counts

14 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(log1p (expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))))
6.0b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
26.9b	(sin (/ x (* y 2.0)))
26.9b	(tan (/ x (* y 2.0)))

rewrite13.0ms

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`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`tan-quot`
1×	`cbrt-undiv` `log1p-udef` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `div-inv` `associate-/l/`

Counts

4 → 60

Calls

4 calls:

1.0ms	(log1p (expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))))
6.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
2.0ms	(sin (/ x (* y 2.0)))
2.0ms	(tan (/ x (* y 2.0)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	159	598
1	450	539
2	1808	539
3	5001	539

prune230.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	71	15	86

Merged error: 24.9b

Counts

86 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(log1p (expm1 (tan (/ x (* y 2.0)))))
6.0b	(/ (log1p (expm1 (tan (/ x (* y 2.0))))) (sin (/ x (* y 2.0))))
26.9b	(sin (/ x (* y 2.0)))
26.9b	(tan (/ x (* y 2.0)))

rewrite10.0ms

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`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
1×	`tan-quot` `cbrt-undiv` `log1p-udef` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

1.0ms	(log1p (expm1 (tan (/ x (* y 2.0)))))
4.0ms	(/ (log1p (expm1 (tan (/ x (* y 2.0))))) (sin (/ x (* y 2.0))))
2.0ms	(sin (/ x (* y 2.0)))
2.0ms	(tan (/ x (* y 2.0)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(log1p (expm1 (tan (/ x (* y 2.0)))))
109.0ms	(/ (log1p (expm1 (tan (/ x (* y 2.0))))) (sin (/ x (* y 2.0))))
9.0ms	(sin (/ x (* y 2.0)))
38.0ms	(tan (/ x (* y 2.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	157	605
1	415	531
2	1749	518
3	5001	512

prune178.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	69	17	86

Merged error: 24.9b

Counts

86 → 17

regimes325.0ms

Accuracy

0% (2.4b remaining)

Error of 27.8b against oracle of 25.4b and baseline of 27.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	0

end0.0ms

sample2.1s

Algorithm

intervals

Results

632.0ms	1382×	body	1280	valid
555.0ms	606×	body	2560	valid
275.0ms	954×	body	640	valid
260.0ms	4206×	body	80	valid
112.0ms	559×	body	320	valid
55.0ms	293×	body	160	valid