Details

sample419.0ms

Algorithm

intervals

Results

224.0ms	83×	body	10240	exit
127.0ms	76×	body	1280	valid
38.0ms	56×	body	640	valid
9.0ms	90×	body	80	valid
5.0ms	16×	body	320	valid
4.0ms	18×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	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: 33.0b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

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`
1×	`expm1-log1p` `expm1-udef`

Counts

3 → 29

Calls

3 calls:

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

series98.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
94.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify50.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	72	248
1	141	216
2	393	216
3	1200	216
4	5001	216

prune137.0ms

Filtered

38 candidates to 28 candidates (73.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	25	13	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	13	39

Merged error: 31.8b

Counts

39 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-exp-log` `log1p-expm1-u` `add-log-exp`
4×	`expm1-log1p-u` `log-pow` `add-cbrt-cube`
3×	`log-prod`
2×	`rem-log-exp`
1×	`expm1-log1p` `rem-exp-log` `expm1-udef`

Counts

4 → 51

Calls

4 calls:

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

series125.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(expm1 (sin (expm1 a)))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
29.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify57.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	103	472
1	199	410
2	488	410
3	1460	410
4	5001	410

prune217.0ms

Filtered

63 candidates to 42 candidates (66.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	55	8	63
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	59	17	76

Merged error: 31.6b

Counts

76 → 17

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

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

series38.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify76.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	43	498
1	64	429
2	83	429
3	124	429
4	224	429
5	546	429
6	2606	429
7	5001	429

prune308.0ms

Filtered

52 candidates to 41 candidates (78.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	42	10	52
Fresh	0	16	16
Picked	1	0	1
Done	0	0	0
Total	43	26	69

Merged error: 31.3b

Counts

69 → 26

localize39.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.9b	(fmod (log (pow (exp (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (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 (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
1.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
1.0ms	(fmod (log (pow (exp (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) a)

series128.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
6.0ms	(fmod (log (pow (exp (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) a)

simplify67.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (60.0ms)

Iter	Nodes	Cost
0	82	735
1	163	637
2	426	483
3	1722	483
4	5002	482

prune261.0ms

Filtered

52 candidates to 41 candidates (78.8%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	25	25
Picked	1	0	1
Done	0	0	0
Total	48	30	78

Merged error: 31.2b

Counts

78 → 30

regimes408.0ms

Accuracy

0% (1.8b remaining)

Error of 33.9b against oracle of 32.1b and baseline of 33.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	30
1	23	30
2	23	30

end0.0ms

sample12.7s

Algorithm

intervals

Results

7.0s	2588×	body	10240	exit
3.7s	2213×	body	1280	valid
1.2s	1708×	body	640	valid
290.0ms	881×	body	320	valid
278.0ms	2731×	body	80	valid
99.0ms	459×	body	160	valid
13.0ms	6×	body	2560	valid
9.0ms	2×	body	5120	valid