Details

sample94.0ms

Algorithm

intervals

Results

37.0ms	52×	body	1280	valid
22.0ms	173×	body	80	valid
13.0ms	33×	body	640	valid
7.0ms	26×	body	320	valid
3.0ms	14×	body	160	valid

simplify10.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

13.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
23.0ms	(/ 1.0 (sin B))
34.0ms	(/ 1.0 (tan B))
113.0ms	(* x (/ 1.0 (tan B)))

simplify49.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	419	664
1	1645	609
2	5001	604

prune302.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`add-exp-log` `times-frac`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `rec-exp` `flip3--` `pow-flip` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

14.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
2.0ms	(/ 1 (sin B))
3.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))

series243.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
13.0ms	(/ 1 (sin B))
43.0ms	(* x (cos B))
95.0ms	(/ (* x (cos B)) (sin B))

simplify41.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	309	612
1	1342	540
2	5002	535

prune217.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

2 → 48

Calls

2 calls:

3.0ms	(* x (cos B))
6.0ms	(/ (- 1 (* x (cos B))) (sin B))

series103.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* x (cos B))
68.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify75.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	195	361
1	793	329
2	3168	329
3	5001	329

prune133.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
59×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log` `associate-/r*`
12×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`div-exp`
6×	`pow1` `div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv`
3×	`associate-r` `associate-l` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

3 → 131

Calls

3 calls:

5.0ms	(/ (sin B) (- 1 (* x (cos B))))
3.0ms	(* x (cos B))
8.0ms	(/ 1 (/ (sin B) (- 1 (* x (cos B)))))

series148.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (sin B) (- 1 (* x (cos B))))
40.0ms	(* x (cos B))
63.0ms	(/ 1 (/ (sin B) (- 1 (* x (cos B)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	498	1423
1	2615	1217
2	5002	1204

prune249.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

0% (0.1b 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	14	6
1	14	6

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	1776×	body	1280	valid
663.0ms	4874×	body	80	valid
565.0ms	1382×	body	640	valid
209.0ms	722×	body	320	valid
77.0ms	358×	body	160	valid