Details

sample312.0ms

Algorithm

intervals

Results

27.0ms	65×	body	1280	valid
11.0ms	164×	body	80	valid
11.0ms	41×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	14×	body	160	valid

simplify16.0ms

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

prune9.0ms

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 4 expressions with local error:

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

rewrite34.0ms

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:

21.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
2.0ms	(/ 1.0 (tan B))
2.0ms	(/ 1.0 (sin B))
6.0ms	(* x (/ 1.0 (tan B)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
36.0ms	(/ 1.0 (tan B))
19.0ms	(/ 1.0 (sin B))
126.0ms	(* x (/ 1.0 (tan B)))

simplify128.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (32.0ms)

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

prune95.0ms

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: 0.1b

Counts

43 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`frac-sub`
10×	`frac-2neg` `clear-num`
8×	`associate-/l*`
4×	`*-commutative`
2×	`div-inv`
1×	`tan-quot` `sub-neg` `flip3--` `associate-/r/` `flip--`

Counts

3 → 28

Calls

3 calls:

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

series254.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
109.0ms	(/ (* x 1.0) (tan B))
19.0ms	(/ 1.0 (sin B))

simplify42.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	312	306
1	1204	289
2	5001	265

prune91.0ms

Filtered

37 candidates to 27 candidates (73.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	37	5	42

Merged error: 0.0b

Counts

42 → 5

localize16.0ms

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))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite18.0ms

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:

8.0ms	(- (/ 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))

series275.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
37.0ms	(* x (cos B))
19.0ms	(/ 1.0 (sin B))
98.0ms	(/ (* x (cos B)) (sin B))

simplify58.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (52.0ms)

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

prune113.0ms

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

localize16.0ms

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))))
8.3b	(/ (* (- 1.0) (- (/ (sin B) (* x (cos B))) (sin B))) (* (- (sin B)) (/ (sin B) (* x (cos B)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(/ (sin B) (* x (cos B)))
4.0ms	(/ (sin B) (* x (cos B)))
5.0ms	(* (- (sin B)) (/ (sin B) (* x (cos B))))
15.0ms	(/ (* (- 1.0) (- (/ (sin B) (* x (cos B))) (sin B))) (* (- (sin B)) (/ (sin B) (* x (cos B)))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (sin B) (* x (cos B)))
66.0ms	(/ (sin B) (* x (cos B)))
80.0ms	(* (- (sin B)) (/ (sin B) (* x (cos B))))
197.0ms	(/ (* (- 1.0) (- (/ (sin B) (* x (cos B))) (sin B))) (* (- (sin B)) (/ (sin B) (* x (cos B)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	357	570
1	1819	543
2	5001	535

prune193.0ms

Filtered

63 candidates to 57 candidates (90.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	63	6	69

Merged error: 0.0b

Counts

69 → 6

regimes57.0ms

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	12	8
1	12	8

end0.0ms

sample1.8s

Algorithm

intervals

Results

733.0ms	1726×	body	1280	valid
379.0ms	1451×	body	640	valid
309.0ms	4933×	body	80	valid
131.0ms	702×	body	320	valid
43.0ms	331×	body	160	valid