Details

sample362.0ms

Algorithm

intervals

Results

173.0ms	64×	body	10240	exit
120.0ms	66×	body	1280	valid
39.0ms	62×	body	640	valid
10.0ms	94×	body	80	valid
7.0ms	22×	body	320	valid
3.0ms	12×	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: 32.4b

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)))
0.2b	(sin (expm1 a))
37.1b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

2×	`expm1-udef`
1×	`sin-diff`

Counts

4 → 2

Calls

4 calls:

1.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
3.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series160.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
85.0ms	(expm1 (sin (expm1 a)))
65.0ms	(sin (expm1 a))
9.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify94.0ms

Algorithm

egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	69	64
1	167	62
2	528	62
3	2130	62
4	5001	62

prune26.0ms

Filtered

14 candidates to 4 candidates (28.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	11	3	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	4	15

Merged error: 32.2b

Counts

15 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (- (exp (sin (expm1 a))) 1) (atan a))
0.2b	(sin (expm1 a))
3.9b	(- (exp (sin (expm1 a))) 1)
20.7b	(fmod (atan2 (- (exp (sin (expm1 a))) 1) (atan a)) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

1×	`sub-neg` `expm1-def` `flip3--` `sin-diff` `flip--` `expm1-udef`

Counts

4 → 6

Calls

4 calls:

1.0ms	(atan2 (- (exp (sin (expm1 a))) 1) (atan a))
2.0ms	(sin (expm1 a))
4.0ms	(- (exp (sin (expm1 a))) 1)
1.0ms	(fmod (atan2 (- (exp (sin (expm1 a))) 1) (atan a)) a)

series152.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (- (exp (sin (expm1 a))) 1) (atan a))
63.0ms	(sin (expm1 a))
84.0ms	(- (exp (sin (expm1 a))) 1)
2.0ms	(fmod (atan2 (- (exp (sin (expm1 a))) 1) (atan a)) a)

simplify40.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	107	97
1	337	93
2	1088	91
3	5002	89

prune33.0ms

Filtered

18 candidates to 5 candidates (27.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	19	3	22

Merged error: 32.2b

Counts

22 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (expm1 (+ (* 2 (sin (expm1 a))) 0)) (+ (exp (sin (expm1 a))) 1))
0.2b	(sin (expm1 a))
0.2b	(sin (expm1 a))
37.1b	(fmod (atan2 (/ (expm1 (+ (* 2 (sin (expm1 a))) 0)) (+ (exp (sin (expm1 a))) 1)) (atan a)) a)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

3×	`expm1-udef`
2×	`associate-/r/` `sin-diff`
1×	`frac-2neg` `flip3-+` `div-sub` `clear-num` `flip-+` `div-inv`

Counts

4 → 8

Calls

4 calls:

4.0ms	(/ (expm1 (+ (* 2 (sin (expm1 a))) 0)) (+ (exp (sin (expm1 a))) 1))
2.0ms	(sin (expm1 a))
2.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (/ (expm1 (+ (* 2 (sin (expm1 a))) 0)) (+ (exp (sin (expm1 a))) 1)) (atan a)) a)

series319.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ (expm1 (+ (* 2 (sin (expm1 a))) 0)) (+ (exp (sin (expm1 a))) 1))
56.0ms	(sin (expm1 a))
62.0ms	(sin (expm1 a))
4.0ms	(fmod (atan2 (/ (expm1 (+ (* 2 (sin (expm1 a))) 0)) (+ (exp (sin (expm1 a))) 1)) (atan a)) a)

simplify44.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	121	162
1	350	156
2	1188	140
3	5001	140

prune68.0ms

Filtered

20 candidates to 12 candidates (60.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	20	3	23

Merged error: 32.2b

Counts

23 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (expm1 a))
0.2b	(sin (expm1 a))
0.4b	(/ (+ (exp (sin (expm1 a))) 1) (expm1 (* 2 (sin (expm1 a)))))
37.1b	(fmod (atan2 (/ 1 (/ (+ (exp (sin (expm1 a))) 1) (expm1 (* 2 (sin (expm1 a)))))) (atan a)) a)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

2×	`sin-diff` `associate-/l/` `expm1-udef`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv`

Counts

4 → 7

Calls

4 calls:

2.0ms	(sin (expm1 a))
2.0ms	(sin (expm1 a))
5.0ms	(/ (+ (exp (sin (expm1 a))) 1) (expm1 (* 2 (sin (expm1 a)))))
1.0ms	(fmod (atan2 (/ 1 (/ (+ (exp (sin (expm1 a))) 1) (expm1 (* 2 (sin (expm1 a)))))) (atan a)) a)

series315.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sin (expm1 a))
55.0ms	(sin (expm1 a))
195.0ms	(/ (+ (exp (sin (expm1 a))) 1) (expm1 (* 2 (sin (expm1 a)))))
4.0ms	(fmod (atan2 (/ 1 (/ (+ (exp (sin (expm1 a))) 1) (expm1 (* 2 (sin (expm1 a)))))) (atan a)) a)

simplify51.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	112	148
1	343	143
2	1361	139
3	5001	139

prune58.0ms

Filtered

19 candidates to 11 candidates (57.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	18	4	22

Merged error: 31.9b

Counts

22 → 4

regimes33.0ms

Accuracy

0% (0.5b remaining)

Error of 33.8b against oracle of 33.3b and baseline of 33.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	25
1	30	25
2	30	25

end0.0ms

sample13.0s

Algorithm

intervals

Results

7.1s	2622×	body	10240	exit
3.8s	2282×	body	1280	valid
1.2s	1672×	body	640	valid
306.0ms	2763×	body	80	valid
285.0ms	851×	body	320	valid
93.0ms	427×	body	160	valid
8.0ms	4×	body	2560	valid
5.0ms	1×	body	5120	valid