Details

sample438.0ms

Algorithm

intervals

Results

245.0ms	91×	body	5120	exit
125.0ms	70×	body	1280	valid
33.0ms	48×	body	640	valid
12.0ms	102×	body	80	valid
8.0ms	24×	body	320	valid
3.0ms	12×	body	160	valid

simplify3.0ms

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: 31.2b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.1b	(sin (expm1 a))
35.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

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

series62.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
57.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify121.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	248
1	44	212
2	54	212
3	68	212
4	114	212
5	228	212
6	919	212
7	3184	212
8	5001	212

prune151.0ms

Filtered

40 candidates to 28 candidates (70.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	28	12	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	12	41

Merged error: 30.0b

Counts

41 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sin (expm1 a))
0.4b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
35.7b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

2.0ms	(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)

series90.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sin (expm1 a))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
28.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify98.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 7 (94.0ms)

Iter	Nodes	Cost
0	63	401
1	92	342
2	121	342
3	180	342
4	339	342
5	863	342
6	3913	342
7	5001	338

prune194.0ms

Filtered

52 candidates to 34 candidates (65.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	44	8	52
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	48	16	64

Merged error: 29.8b

Counts

64 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
35.7b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
35.7b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
35.7b	(fmod (log (exp (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` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`exp-prod`
1×	`rem-exp-log`

Counts

4 → 32

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)

series35.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(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

44 → 44

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	430
1	60	361
2	78	361
3	118	361
4	218	361
5	534	361
6	2589	361
7	5001	361

prune261.0ms

Filtered

44 candidates to 33 candidates (75.0%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	37	7	44
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	39	21	60

Merged error: 29.6b

Counts

60 → 21

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
35.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
35.7b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
35.7b	(fmod (log (exp (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` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`exp-prod`
1×	`rem-exp-log`

Counts

4 → 32

Calls

4 calls:

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

series35.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (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)

simplify75.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	47	370
1	63	319
2	81	319
3	121	319
4	221	319
5	537	319
6	2592	319
7	5001	319

prune190.0ms

Filtered

44 candidates to 32 candidates (72.7%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	37	7	44
Fresh	4	16	20
Picked	1	0	1
Done	0	0	0
Total	42	23	65

Merged error: 29.5b

Counts

65 → 23

regimes311.0ms

Accuracy

0% (1.7b remaining)

Error of 33.2b against oracle of 31.4b and baseline of 33.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	37
1	23	37

end0.0ms

sample12.9s

Algorithm

intervals

Results

7.0s	2570×	body	5120	exit
3.9s	2281×	body	1280	valid
1.1s	1587×	body	640	valid
313.0ms	2839×	body	80	valid
296.0ms	846×	body	320	valid
103.0ms	442×	body	160	valid
25.0ms	5×	body	5120	valid