Details

sample65.0ms

Algorithm

intervals

Results

22.0ms	51×	body	1280	valid
12.0ms	44×	body	640	valid
10.0ms	160×	body	80	valid
7.0ms	23×	body	320	valid
3.0ms	20×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (tan B))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

2×	`frac-2neg` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 8

Calls

3 calls:

2.0ms	(/ 1.0 (sin B))
1.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (tan B))

series160.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ 1.0 (sin B))
103.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
38.0ms	(/ 1.0 (tan B))

simplify121.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 4 (45.0ms)

Iter	Nodes	Cost
0	100	66
1	215	65
2	653	65
3	1962	60
4	4633	57
5	5001	57

prune47.0ms

Filtered

17 candidates to 13 candidates (76.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	14	3	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	4	18

Merged error: 0.1b

Counts

18 → 4

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (cos B) (sin B))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

2×	`frac-2neg` `clear-num` `div-inv`
1×	`fma-udef`

Counts

3 → 7

Calls

3 calls:

1.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
3.0ms	(/ (cos B) (sin B))

series136.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
19.0ms	(/ (cos B) (sin B))

simplify107.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 4 (45.0ms)

Iter	Nodes	Cost
0	95	66
1	221	65
2	680	65
3	2044	60
4	4694	57
5	5001	57

prune36.0ms

Filtered

16 candidates to 10 candidates (62.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	16	4	20

Merged error: 0.1b

Counts

20 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (cos B))
0.1b	(/ 1.0 (sin B))
0.2b	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`frac-times`
4×	`flip3--` `frac-2neg` `clear-num` `flip--`
3×	`associate-*l/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r/` `-commutative` `div-inv`
1×	`associate-l`

Counts

3 → 21

Calls

3 calls:

2.0ms	(* x (cos B))
2.0ms	(/ 1.0 (sin B))
5.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

series149.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* x (cos B))
19.0ms	(/ 1.0 (sin B))
91.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

simplify96.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	211	190
1	1019	185
2	4524	176
3	5001	176

prune69.0ms

Filtered

30 candidates to 21 candidates (70.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	30	4	34

Merged error: 0.1b

Counts

34 → 4

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (cos B))
0.2b	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-r/` `-commutative` `associate-/l/` `associate-/l*`
1×	`flip3--` `frac-2neg` `clear-num` `flip--` `div-inv`

Counts

2 → 8

Calls

2 calls:

2.0ms	(* x (cos B))
5.0ms	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))

series119.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(* x (cos B))
79.0ms	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))

simplify93.0ms

Algorithm

egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 4 (91.0ms)

Iter	Nodes	Cost
0	103	63
1	365	62
2	1349	59
3	4792	53
4	5001	52

prune28.0ms

Filtered

14 candidates to 10 candidates (71.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	14	4	18

Merged error: 0.1b

Counts

18 → 4

regimes38.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	6
1	14	6

end0.0ms

sample1.8s

Algorithm

intervals

Results

707.0ms	1656×	body	1280	valid
381.0ms	1421×	body	640	valid
311.0ms	5083×	body	80	valid
129.0ms	679×	body	320	valid
44.0ms	334×	body	160	valid