Details

sample58.0ms

Algorithm

intervals

Results

21.0ms	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

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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

localize10.0ms

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:

10.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
3.0ms	(* x (/ 1.0 (tan B)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
18.0ms	(/ 1.0 (sin B))
34.0ms	(/ 1.0 (tan B))
108.0ms	(* x (/ 1.0 (tan B)))

simplify117.0ms

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

prune85.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`frac-sub`
17×	`associate-*r/`
14×	`clear-num`
13×	`frac-2neg`
8×	`associate-/l*`
5×	`*-commutative` `div-inv`
3×	`un-div-inv`
2×	`sub-div`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `associate-r` `flip--` `distribute-lft-out--`

Counts

4 → 35

Calls

4 calls:

7.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
2.0ms	(* x (cos B))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x (cos B)) (sin B))

series258.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
37.0ms	(* x (cos B))
18.0ms	(/ 1.0 (sin B))
92.0ms	(/ (* x (cos B)) (sin B))

simplify52.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	344	422
1	1745	396
2	5002	389

prune101.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	46	6	52

Merged error: 0.0b

Counts

52 → 6

localize12.0ms

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) (/ (sin B) (* x (cos B))))
7.8b	(/ (* 1.0 (- (/ (sin B) (* x (cos B))) (sin B))) (* (sin B) (/ (sin B) (* x (cos B)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-r/` `-commutative`
11×	`associate-/r*`
7×	`clear-num` `div-inv`
6×	`times-frac` `associate-/r/`
5×	`frac-2neg`
4×	`associate-r`
2×	`un-div-inv` `associate-/l/` `associate-/l*`
1×	`flip3--` `flip--`

Counts

4 → 40

Calls

4 calls:

4.0ms	(/ (sin B) (* x (cos B)))
3.0ms	(/ (sin B) (* x (cos B)))
5.0ms	(* (sin B) (/ (sin B) (* x (cos B))))
12.0ms	(/ (* 1.0 (- (/ (sin B) (* x (cos B))) (sin B))) (* (sin B) (/ (sin B) (* x (cos B)))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (sin B) (* x (cos B)))
61.0ms	(/ (sin B) (* x (cos B)))
68.0ms	(* (sin B) (/ (sin B) (* x (cos B))))
213.0ms	(/ (* 1.0 (- (/ (sin B) (* x (cos B))) (sin B))) (* (sin B) (/ (sin B) (* x (cos B)))))

simplify39.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	264	390
1	1231	375
2	5002	366

prune155.0ms

Filtered

52 candidates to 45 candidates (86.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	48	4	52
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	51	7	58

Merged error: 0.0b

Counts

58 → 7

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	(* (+ (* 1.0 (* 1 (/ 1 (* x (cos B))))) (- 1.0)) (/ (* x (cos B)) (sin B)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 33

Calls

4 calls:

2.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))
3.0ms	(/ 1 (* x (cos B)))
12.0ms	(* (+ (* 1.0 (* 1 (/ 1 (* x (cos B))))) (- 1.0)) (/ (* x (cos B)) (sin B)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* x (cos B))
91.0ms	(/ (* x (cos B)) (sin B))
45.0ms	(/ 1 (* x (cos B)))
132.0ms	(* (+ (* 1.0 (* 1 (/ 1 (* x (cos B))))) (- 1.0)) (/ (* x (cos B)) (sin B)))

simplify36.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	222	456
1	1026	441
2	5002	396

prune185.0ms

Filtered

45 candidates to 37 candidates (82.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	45	7	52

Merged error: 0b

Counts

52 → 7

regimes61.0ms

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

679.0ms	1656×	body	1280	valid
366.0ms	1421×	body	640	valid
303.0ms	5083×	body	80	valid
124.0ms	679×	body	320	valid
45.0ms	334×	body	160	valid