Details

sample413.0ms

Algorithm

intervals

Results

203.0ms	80×	body	10240	exit
142.0ms	77×	body	1280	valid
37.0ms	48×	body	640	valid
9.0ms	99×	body	80	valid
7.0ms	24×	body	320	valid
2.0ms	8×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(sin (expm1 a))
36.9b	(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	(expm1 (sin (expm1 a)))
1.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series63.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
57.0ms	(sin (expm1 a))
3.0ms	(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

prune156.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 30.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (expm1 a))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.8b	(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:

54.0ms	(sin (expm1 a))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
32.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify100.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 7 (95.0ms)

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

prune206.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 30.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.8b	(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)

series37.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(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)
3.0ms	(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

prune275.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 30.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.8b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.9b	(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` `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 (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 (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify77.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 1 (4.0ms)

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

prune207.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 30.2b

regimes302.0ms

Accuracy

0% (1.8b remaining)

Error of 33.4b against oracle of 31.6b and baseline of 33.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	30
1	23	30

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.6s	2624×	body	10240	exit
3.8s	2299×	body	1280	valid
1.1s	1616×	body	640	valid
265.0ms	848×	body	320	valid
265.0ms	2813×	body	80	valid
84.0ms	416×	body	160	valid
14.0ms	3×	body	5120	valid
9.0ms	5×	body	2560	valid