Details

sample344.0ms

Algorithm

intervals

Results

158.0ms	59×	body	5120	exit
119.0ms	68×	body	1280	valid
32.0ms	46×	body	640	valid
11.0ms	97×	body	80	valid
11.0ms	30×	body	320	valid
3.0ms	15×	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: 31.8b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

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)

series145.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
84.0ms	(expm1 (sin (expm1 a)))
57.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify124.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	108	302
1	242	264
2	720	264
3	2933	264
4	5001	264

prune193.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	37	14	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	14	52

Merged error: 30.8b

Counts

52 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite9.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 69

Calls

4 calls:

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

series144.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	94	1009
1	316	926
2	1541	829
3	5002	812

prune307.0ms

Filtered

81 candidates to 54 candidates (66.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	74	7	81
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	77	18	95

Merged error: 30.8b

Counts

95 → 18

localize21.0ms

Local error

Found 4 expressions with local error:

36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

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

series9.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify96.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	408
1	19	356
2	23	356
3	28	356
4	47	356
5	101	356
6	507	356
7	1681	356
8	5001	356

prune271.0ms

Filtered

48 candidates to 36 candidates (75.0%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	45	21	66

Merged error: 30.8b

Counts

66 → 21

localize27.0ms

Local error

Found 4 expressions with local error:

36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

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

series9.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify95.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	408
1	19	356
2	23	356
3	28	356
4	47	356
5	101	356
6	507	356
7	1681	356
8	5001	356

prune223.0ms

Filtered

48 candidates to 36 candidates (75.0%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	2	17	19
Picked	1	0	1
Done	0	1	1
Total	47	22	69

Merged error: 30.7b

Counts

69 → 22

regimes240.0ms

Accuracy

0% (1.3b remaining)

Error of 33.5b against oracle of 32.3b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	70
1	23	70

end0.0ms

sample13.0s

Algorithm

intervals

Results

7.0s	2570×	body	5120	exit
3.8s	2224×	body	1280	valid
1.2s	1666×	body	640	valid
308.0ms	2796×	body	80	valid
308.0ms	862×	body	320	valid
104.0ms	446×	body	160	valid
20.0ms	4×	body	5120	valid
4.0ms	2×	body	2560	valid