Details

sample347.0ms

Algorithm

intervals

Results

35.0ms	52×	body	1280	valid
21.0ms	173×	body	80	valid
13.0ms	33×	body	640	valid
7.0ms	26×	body	320	valid
3.0ms	14×	body	160	valid

simplify13.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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)))

rewrite38.0ms

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:

9.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
21.0ms	(* x (/ 1.0 (tan B)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
38.0ms	(/ 1.0 (tan B))
122.0ms	(* 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

prune306.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `associate-/r*`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `frac-add` `-commutative` `flip-+` `distribute-neg-frac` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

8.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
3.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))

series248.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
37.0ms	(* x (cos B))
93.0ms	(/ (* x (cos B)) (sin B))

simplify44.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	359	603
1	1463	536
2	5002	530

prune238.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ (sin B) (* x (cos B)))
0.1b	(* x (cos B))
0.3b	(/ 1 (/ (sin B) (* x (cos B))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
34×	`add-exp-log` `add-sqr-sqrt`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv`
7×	`pow1` `div-inv`
5×	`prod-exp`
4×	`add-log-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `associate-r` `associate-l` `clear-num` `cbrt-unprod`
1×	`pow-flip` `pow-prod-down` `associate-/r/` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (sin B) (* x (cos B)))
3.0ms	(* x (cos B))
7.0ms	(/ 1 (/ (sin B) (* x (cos B))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
62.0ms	(/ (sin B) (* x (cos B)))
34.0ms	(* x (cos B))
72.0ms	(/ 1 (/ (sin B) (* x (cos B))))

simplify47.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	419	846
1	1818	733
2	5001	690

prune285.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.2b	(/ (sin B) x)
0.2b	(/ (/ (sin B) x) (cos B))
0.3b	(/ 1 (/ (/ (sin B) x) (cos B)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

486×	`times-frac`
246×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
52×	`associate-/r*`
34×	`add-exp-log`
24×	`div-inv`
22×	`add-cbrt-cube` `associate-/l*`
20×	`div-exp`
11×	`cbrt-undiv`
5×	`pow1`
4×	`frac-2neg` `clear-num` `add-log-exp`
3×	`rec-exp` `1-exp`
1×	`pow-flip` `associate-/r/` `associate-/l/` `inv-pow`

Counts

4 → 324

Calls

4 calls:

2.0ms	(/ 1.0 (sin B))
3.0ms	(/ (sin B) x)
6.0ms	(/ (/ (sin B) x) (cos B))
13.0ms	(/ 1 (/ (/ (sin B) x) (cos B)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1.0 (sin B))
27.0ms	(/ (sin B) x)
64.0ms	(/ (/ (sin B) x) (cos B))
74.0ms	(/ 1 (/ (/ (sin B) x) (cos B)))

simplify55.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1161	3556
1	5001	3208

prune866.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	9
1	22	9
2	28	9
3	28	9

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	1776×	body	1280	valid
632.0ms	4874×	body	80	valid
534.0ms	1382×	body	640	valid
200.0ms	722×	body	320	valid
76.0ms	358×	body	160	valid