Details

sample407.0ms

Algorithm

intervals

Results

210.0ms	78×	body	10240	exit
123.0ms	80×	body	1280	valid
43.0ms	59×	body	640	valid
9.0ms	27×	body	320	valid
9.0ms	84×	body	80	valid
2.0ms	1×	body	2560	valid
1.0ms	5×	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: 34.9b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.5b	(sin (expm1 a))
39.7b	(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	(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)

series62.0ms

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

simplify118.0ms

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

prune174.0ms

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: 33.7b

Counts

41 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(sin (expm1 a))
0.5b	(sin (expm1 a))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 61

Calls

4 calls:

2.0ms	(sin (expm1 a))
2.0ms	(sin (expm1 a))
6.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series301.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sin (expm1 a))
60.0ms	(sin (expm1 a))
182.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify60.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	101	595
1	312	528
2	1529	489
3	5001	468

prune301.0ms

Filtered

73 candidates to 46 candidates (63.0%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	60	13	73
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	61	24	85

Merged error: 33.2b

Counts

85 → 24

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 61

Calls

4 calls:

6.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series191.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify59.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	96	883
1	299	760
2	1488	725
3	5001	688

prune454.0ms

Filtered

73 candidates to 49 candidates (67.1%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	62	11	73
Fresh	1	21	22
Picked	1	0	1
Done	0	1	1
Total	64	33	97

Merged error: 32.9b

Counts

97 → 33

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
39.8b	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite7.0ms

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`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 30

Calls

4 calls:

5.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series197.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
2.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify101.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	58	834
1	85	686
2	161	532
3	428	505
4	1891	505
5	5001	505

prune220.0ms

Filtered

42 candidates to 30 candidates (71.4%)

Pruning

39 alts after pruning (37 fresh and 2 done)

	Pruned	Kept	Total
New	34	8	42
Fresh	2	29	31
Picked	0	1	1
Done	0	1	1
Total	36	39	75

Merged error: 32.8b

Counts

75 → 39

regimes531.0ms

Accuracy

0% (2.1b remaining)

Error of 33.7b against oracle of 31.7b and baseline of 33.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	70
1	26	70

end0.0ms

sample12.9s

Algorithm

intervals

Results

7.1s	2594×	body	10240	exit
3.8s	2256×	body	1280	valid
1.2s	1758×	body	640	valid
289.0ms	2768×	body	80	valid
259.0ms	778×	body	320	valid
95.0ms	436×	body	160	valid
6.0ms	3×	body	2560	valid
5.0ms	1×	body	5120	valid