Details

sample413.0ms

Algorithm

intervals

Results

226.0ms	83×	body	10240	exit
111.0ms	69×	body	1280	valid
41.0ms	60×	body	640	valid
11.0ms	33×	body	320	valid
9.0ms	78×	body	80	valid
3.0ms	16×	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 (100.0%)

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: 35.8b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
41.2b	(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)

series169.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(sin (expm1 a))
104.0ms	(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	97	215
1	226	188
2	679	188
3	2829	188
4	5001	188

prune135.0ms

Filtered

39 candidates to 30 candidates (23.1%)

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: 34.9b

Counts

40 → 10

localize18.0ms

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))))
41.2b	(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)

series549.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt (expm1 (sin (expm1 a))))
182.0ms	(cbrt (expm1 (sin (expm1 a))))
182.0ms	(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)

simplify71.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (66.0ms)

Iter	Nodes	Cost
0	88	549
1	181	487
2	472	481
3	1558	470
4	5001	467

prune247.0ms

Filtered

60 candidates to 44 candidates (26.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	48	12	60
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	50	20	70

Merged error: 34.4b

Counts

70 → 20

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

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:

1.0ms	(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)

series135.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(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)

simplify243.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	38	471
1	67	393
2	144	391
3	570	391
4	4356	391
5	5001	391

prune243.0ms

Filtered

52 candidates to 39 candidates (25.0%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	2	16	18
Picked	0	1	1
Done	0	1	1
Total	48	24	72

Merged error: 34.4b

Counts

72 → 24

localize20.0ms

Local error

Found 4 expressions with local error:

41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.2b	(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)

simplify95.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (3.0ms)

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	1687	356
8	5001	356

prune172.0ms

Filtered

48 candidates to 36 candidates (25.0%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	21	21
Picked	1	0	1
Done	1	1	2
Total	47	25	72

Merged error: 34.4b

Counts

72 → 25

regimes418.0ms

Accuracy

0% (1.2b remaining)

Error of 33.5b against oracle of 32.3b and baseline of 33.5b

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

7.1s	2613×	body	10240	exit
3.7s	2260×	body	1280	valid
1.1s	1633×	body	640	valid
288.0ms	866×	body	320	valid
287.0ms	2795×	body	80	valid
107.0ms	440×	body	160	valid
15.0ms	3×	body	5120	valid
6.0ms	3×	body	2560	valid