Details

sample445.0ms

Algorithm

intervals

Results

241.0ms	87×	body	10240	exit
140.0ms	87×	body	1280	valid
34.0ms	50×	body	640	valid
9.0ms	85×	body	80	valid
8.0ms	25×	body	320	valid
2.0ms	9×	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: 34.6b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
40.0b	(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:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(sin (expm1 a))
1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify122.0ms

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

prune159.0ms

Filtered

40 candidates to 28 candidates (70.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	27	13	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	13	41

Merged error: 33.4b

Counts

41 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
40.0b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite8.0ms

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:

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

series34.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify96.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 7 (92.0ms)

Iter	Nodes	Cost
0	59	434
1	89	373
2	116	373
3	169	373
4	318	373
5	822	373
6	3775	373
7	5001	369

prune203.0ms

Filtered

52 candidates to 33 candidates (63.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	50	15	65

Merged error: 33.1b

Counts

65 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
40.0b	(fmod (log (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)

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` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

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

series335.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
109.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
113.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (log (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)

simplify110.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	42	648
1	81	562
2	190	556
3	656	539
4	3491	539
5	5001	539

prune261.0ms

Filtered

52 candidates to 37 candidates (71.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	48	19	67

Merged error: 33.1b

Counts

67 → 19

localize30.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
40.0b	(fmod (log (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)
40.0b	(fmod (log (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)
40.0b	(fmod (log (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` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

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

series117.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (log (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)
3.0ms	(fmod (log (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)
3.0ms	(fmod (log (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)

simplify111.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	42	904
1	81	750
2	190	748
3	656	697
4	3491	697
5	5001	697

prune218.0ms

Filtered

44 candidates to 34 candidates (77.3%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	38	6	44
Fresh	0	18	18
Picked	0	1	1
Done	0	0	0
Total	38	25	63

Merged error: 32.9b

Counts

63 → 25

regimes339.0ms

Accuracy

0% (1.6b remaining)

Error of 33.6b against oracle of 32.0b and baseline of 33.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	58
1	21	58

end0.0ms

sample13.4s

Algorithm

intervals

Results

7.4s	2710×	body	10240	exit
3.9s	2336×	body	1280	valid
1.1s	1636×	body	640	valid
298.0ms	2792×	body	80	valid
281.0ms	783×	body	320	valid
98.0ms	444×	body	160	valid
24.0ms	5×	body	5120	valid
8.0ms	4×	body	2560	valid