Details

sample62.0ms

Algorithm

intervals

Results

26.0ms	65×	body	1280	valid
10.0ms	41×	body	640	valid
10.0ms	164×	body	80	valid
3.0ms	18×	body	320	valid
2.0ms	14×	body	160	valid

simplify11.0ms

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

prune5.0ms

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

localize14.0ms

Local error

Found 3 expressions with local error:

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

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

series153.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
36.0ms	(/ 1.0 (tan B))
19.0ms	(/ 1.0 (sin B))

simplify109.0ms

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

prune42.0ms

Filtered

17 candidates to 13 candidates (76.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	3	18

Merged error: 0.1b

Counts

18 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

3×	`frac-2neg` `associate-*l/` `clear-num` `div-inv`
1×	`associate-l` `*-commutative` `fma-udef`

Counts

4 → 12

Calls

4 calls:

1.0ms	(fma (- x) (* (/ 1.0 (sin B)) (cos B)) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (sin B))
4.0ms	(* (/ 1.0 (sin B)) (cos B))

series169.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(fma (- x) (* (/ 1.0 (sin B)) (cos B)) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
18.0ms	(/ 1.0 (sin B))
38.0ms	(* (/ 1.0 (sin B)) (cos B))

simplify62.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 4 (57.0ms)

Iter	Nodes	Cost
0	106	84
1	319	83
2	1053	83
3	2461	78
4	5002	74

prune51.0ms

Filtered

24 candidates to 16 candidates (66.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	24	3	27

Merged error: 0.1b

Counts

27 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (cos B))
0.2b	(/ 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))))

series127.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* x (cos B))
18.0ms	(/ 1.0 (sin B))
73.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

simplify97.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (28.0ms)

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

prune70.0ms

Filtered

30 candidates to 21 candidates (70.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	27	6	33

Merged error: 0.1b

Counts

33 → 6

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 11

Calls

2 calls:

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

series109.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(* x (cos B))
75.0ms	(/ (- 1 (* x (cos B))) (/ (sin B) 1.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	116	82
1	497	79
2	2126	76
3	5002	74

prune37.0ms

Filtered

17 candidates to 13 candidates (76.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	2	0	2
Picked	0	1	1
Done	1	2	3
Total	18	5	23

Merged error: 0.1b

Counts

23 → 5

regimes41.0ms

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	13	6
1	13	6

end0.0ms

sample1.8s

Algorithm

intervals

Results

722.0ms	1726×	body	1280	valid
378.0ms	1451×	body	640	valid
294.0ms	4933×	body	80	valid
125.0ms	702×	body	320	valid
42.0ms	331×	body	160	valid