Details

sample434.0ms

Algorithm

intervals

Results

224.0ms	81×	body	5120	exit
133.0ms	81×	body	1280	valid
40.0ms	57×	body	640	valid
9.0ms	25×	body	320	valid
8.0ms	76×	body	80	valid
4.0ms	17×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune5.0ms

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: 36.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.3b	(sin (expm1 a))
41.3b	(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)))
1.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series15.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
11.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify117.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (2.0ms)

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

prune184.0ms

Filtered

40 candidates to 28 candidates (30.0%)

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: 34.6b

Counts

41 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (expm1 a))
0.6b	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
41.3b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 58

Calls

4 calls:

2.0ms	(sin (expm1 a))
2.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
2.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series22.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sin (expm1 a))
1.0ms	(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
8.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify128.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	112	584
1	390	527
2	2787	521
3	5001	521

prune269.0ms

Filtered

70 candidates to 35 candidates (50.0%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	63	19	82

Merged error: 34.4b

Counts

82 → 19

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
41.3b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
41.3b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
41.3b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 44

Calls

4 calls:

2.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series14.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify126.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	88	540
1	337	452
2	2685	448
3	5002	448

prune295.0ms

Filtered

56 candidates to 36 candidates (35.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	1	16	17
Picked	1	0	1
Done	1	0	1
Total	54	21	75

Merged error: 34.2b

Counts

75 → 21

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
41.3b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
41.3b	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
41.3b	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 44

Calls

4 calls:

2.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
1.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
1.0ms	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

series14.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
2.0ms	(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)
2.0ms	(fmod (cbrt (cbrt (pow (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) 3))) a)

simplify127.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	102	534
1	361	452
2	2849	448
3	5003	448

prune203.0ms

Filtered

56 candidates to 34 candidates (39.3%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	20	20
Picked	0	1	1
Done	0	0	0
Total	54	23	77

Merged error: 34.2b

Counts

77 → 23

regimes413.0ms

Accuracy

0% (1.6b remaining)

Error of 33.6b against oracle of 31.9b and baseline of 33.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	32
1	20	32

end0.0ms

sample13.2s

Algorithm

intervals

Results

7.2s	2626×	body	5120	exit
3.9s	2301×	body	1280	valid
1.1s	1639×	body	640	valid
310.0ms	2791×	body	80	valid
281.0ms	820×	body	320	valid
100.0ms	444×	body	160	valid
14.0ms	3×	body	5120	valid
4.0ms	2×	body	2560	valid

Details

sample434.0ms

simplify2.0ms

prune5.0ms

localize12.0ms

rewrite4.0ms

series15.0ms

simplify117.0ms

prune184.0ms

localize16.0ms

rewrite8.0ms

series22.0ms

simplify128.0ms

prune269.0ms

localize25.0ms

rewrite5.0ms

series14.0ms

simplify126.0ms

prune295.0ms

localize35.0ms

rewrite5.0ms

series14.0ms

simplify127.0ms

prune203.0ms

regimes413.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample13.2s

Profiling