Details

sample439.0ms

Algorithm

intervals

Results

243.0ms	90×	body	10240	exit
119.0ms	76×	body	1280	valid
44.0ms	60×	body	640	valid
9.0ms	28×	body	320	valid
9.0ms	78×	body	80	valid
3.0ms	14×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune4.0ms

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: 35.5b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log1p-expm1-u`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

3 → 30

Calls

3 calls:

2.0ms	(sin (expm1 a))
1.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series153.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(sin (expm1 a))
89.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify118.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	215
1	231	188
2	706	188
3	2916	188
4	5002	188

prune165.0ms

Filtered

39 candidates to 30 candidates (76.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	30	9	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	10	40

Merged error: 34.6b

Counts

40 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

4.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series122.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify248.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	38	471
1	67	393
2	144	391
3	589	391
4	4672	391
5	5001	391

prune267.0ms

Filtered

52 candidates to 39 candidates (75.0%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	45	7	52
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	46	16	62

Merged error: 34.6b

Counts

62 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (expm1 (sin (expm1 a))))
0.5b	(cbrt (expm1 (sin (expm1 a))))
0.5b	(cbrt (expm1 (sin (expm1 a))))
40.9b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series516.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt (expm1 (sin (expm1 a))))
170.0ms	(cbrt (expm1 (sin (expm1 a))))
170.0ms	(cbrt (expm1 (sin (expm1 a))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify70.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (65.0ms)

Iter	Nodes	Cost
0	88	549
1	181	487
2	472	481
3	1562	470
4	5001	467

prune342.0ms

Filtered

60 candidates to 44 candidates (73.3%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	47	13	60
Fresh	0	13	13
Picked	0	1	1
Done	1	1	2
Total	48	28	76

Merged error: 34.2b

Counts

76 → 28

localize24.0ms

Local error

Found 4 expressions with local error:

40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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`

Counts

4 → 36

Calls

4 calls:

1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series8.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify94.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	17	408
1	19	356
2	23	356
3	28	356
4	47	356
5	101	356
6	507	356
7	1681	356
8	5001	356

prune223.0ms

Filtered

48 candidates to 36 candidates (75.0%)

Pruning

32 alts after pruning (29 fresh and 3 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	1	24	25
Picked	0	1	1
Done	0	2	2
Total	44	32	76

Merged error: 34.2b

Counts

76 → 32

regimes564.0ms

Accuracy

0% (1.2b remaining)

Error of 34.0b against oracle of 32.8b and baseline of 34.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7

end0.0ms

sample12.9s

Algorithm

intervals

Results

6.9s	2544×	body	10240	exit
4.0s	2326×	body	1280	valid
1.1s	1637×	body	640	valid
286.0ms	2707×	body	80	valid
284.0ms	854×	body	320	valid
104.0ms	474×	body	160	valid
5.0ms	1×	body	5120	valid
2.0ms	1×	body	2560	valid