Details

sample313.0ms

Algorithm

intervals

Results

23.0ms	51×	body	1280	valid
11.0ms	44×	body	640	valid
9.0ms	160×	body	80	valid
4.0ms	23×	body	320	valid
2.0ms	20×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	31	6
2	39	6
3	50	6
4	53	6
5	53	6

prune8.0ms

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

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`clear-num`
12×	`associate-*r/` `frac-sub`
10×	`frac-2neg`
4×	`un-div-inv`
3×	`div-inv`
2×	`tan-quot` `associate-r` `associate-/r/`
1×	`sub-neg` `flip3--` `*-commutative` `flip--`

Counts

4 → 30

Calls

4 calls:

7.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
6.0ms	(* x (/ 1.0 (tan B)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
19.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))
134.0ms	(* x (/ 1.0 (tan B)))

simplify120.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	283	281
1	980	265
2	4521	246
3	5001	246

prune93.0ms

Filtered

42 candidates to 28 candidates (66.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	5	43

Merged error: 0.0b

Counts

43 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b	(* x (cos B))
0.1b	(/ 1 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`frac-sub`
12×	`frac-2neg`
10×	`clear-num`
8×	`associate-/l*`
5×	`*-commutative`
4×	`div-inv`
2×	`sub-div`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `flip--` `inv-pow`

Counts

4 → 32

Calls

4 calls:

7.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
2.0ms	(* x (cos B))
2.0ms	(/ 1 (sin B))
4.0ms	(/ (* x (cos B)) (sin B))

series239.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
40.0ms	(* x (cos B))
13.0ms	(/ 1 (sin B))
94.0ms	(/ (* x (cos B)) (sin B))

simplify38.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	267	327
1	925	299
2	5001	296

prune89.0ms

Filtered

44 candidates to 27 candidates (61.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	42	7	49

Merged error: 0.0b

Counts

49 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin B) (* x (cos B)))
0.2b	(/ (sin B) (* x (cos B)))
0.3b	(* (/ (sin B) (* x (cos B))) (sin B))
7.8b	(/ (- (/ (sin B) (* x (cos B))) (sin B)) (* (/ (sin B) (* x (cos B))) (sin B)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`associate-/r*`
10×	`associate-*l/`
6×	`*-commutative`
5×	`frac-2neg` `clear-num` `associate-/r/` `div-inv`
2×	`associate-l` `associate-/l/`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 31

Calls

4 calls:

4.0ms	(/ (sin B) (* x (cos B)))
4.0ms	(/ (sin B) (* x (cos B)))
5.0ms	(* (/ (sin B) (* x (cos B))) (sin B))
11.0ms	(/ (- (/ (sin B) (* x (cos B))) (sin B)) (* (/ (sin B) (* x (cos B))) (sin B)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (sin B) (* x (cos B)))
64.0ms	(/ (sin B) (* x (cos B)))
72.0ms	(* (/ (sin B) (* x (cos B))) (sin B))
183.0ms	(/ (- (/ (sin B) (* x (cos B))) (sin B)) (* (/ (sin B) (* x (cos B))) (sin B)))

simplify43.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	217	291
1	1132	271
2	5001	251

prune127.0ms

Filtered

43 candidates to 34 candidates (79.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	39	4	43
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	42	8	50

Merged error: 0b

Counts

50 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))
0.2b	(/ 1 (* x (cos B)))
0.5b	(* (- (/ (/ 1 (* x (cos B))) 1) 1) (/ (* x (cos B)) (sin B)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`frac-times`
8×	`associate-/l*`
7×	`*-commutative`
6×	`flip3--` `clear-num` `flip--`
5×	`frac-2neg` `associate-*r/`
3×	`div-inv`
2×	`associate-l/` `associate-/r`
1×	`associate-r` `un-div-inv` `inv-pow`

Counts

4 → 32

Calls

4 calls:

2.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))
4.0ms	(/ 1 (* x (cos B)))
11.0ms	(* (- (/ (/ 1 (* x (cos B))) 1) 1) (/ (* x (cos B)) (sin B)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* x (cos B))
96.0ms	(/ (* x (cos B)) (sin B))
47.0ms	(/ 1 (* x (cos B)))
128.0ms	(* (- (/ (/ 1 (* x (cos B))) 1) 1) (/ (* x (cos B)) (sin B)))

simplify33.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	179	368
1	955	355
2	5002	317

prune112.0ms

Filtered

44 candidates to 35 candidates (79.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	3	2	5
Picked	0	1	1
Done	1	1	2
Total	45	7	52

Merged error: 0b

Counts

52 → 7

regimes58.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	6
1	10	6

end0.0ms

sample1.7s

Algorithm

intervals

Results

695.0ms	1656×	body	1280	valid
369.0ms	1421×	body	640	valid
314.0ms	5083×	body	80	valid
128.0ms	679×	body	320	valid
42.0ms	334×	body	160	valid