Details

sample72.0ms

Algorithm

intervals

Results

27.0ms	55×	body	1280	valid
13.0ms	152×	body	80	valid
12.0ms	38×	body	640	valid
6.0ms	27×	body	320	valid
2.0ms	12×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune7.0ms

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

rewrite25.0ms

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:

8.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (tan B))
4.0ms	(/ 1.0 (sin B))
7.0ms	(* x (/ 1.0 (tan B)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
34.0ms	(/ 1.0 (tan B))
18.0ms	(/ 1.0 (sin B))
112.0ms	(* x (/ 1.0 (tan B)))

simplify47.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (39.0ms)

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

prune297.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 107

Calls

4 calls:

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

series191.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
18.0ms	(/ 1.0 (sin B))
102.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
53.0ms	(* x (/ 1.0 (sin B)))

simplify46.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	315	645
1	1562	560
2	5001	560

prune288.0ms

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`times-frac`
8×	`add-log-exp`
7×	`associate-l`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`associate-/l*`
3×	`associate-r` `div-inv`
2×	`frac-2neg` `associate-*l/` `clear-num` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

8.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
5.0ms	(/ (* x 1.0) (sin B))
4.0ms	(/ 1.0 (sin B))
7.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series277.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
56.0ms	(/ (* x 1.0) (sin B))
18.0ms	(/ 1.0 (sin B))
101.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify55.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	422	714
1	1971	620
2	5001	614

prune255.0ms

Pruning

9 alts after pruning (9 fresh and 0 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 1.0))
0.2b	(* (/ 1 (/ (sin B) (* x 1.0))) (cos B))
0.3b	(/ 1 (/ (sin B) (* x 1.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

77×	`times-frac`
64×	`add-exp-log`
52×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
45×	`add-cube-cbrt`
34×	`add-cbrt-cube`
27×	`div-exp`
26×	`associate-l`
17×	`prod-exp`
13×	`cbrt-undiv`
11×	`associate-/r*` `div-inv`
9×	`associate-/l*`
7×	`pow1` `cbrt-unprod`
6×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `unswap-sqr`
2×	`associate-/r/`
1×	`pow-flip` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 160

Calls

4 calls:

3.0ms	(/ 1.0 (sin B))
5.0ms	(/ (sin B) (* x 1.0))
15.0ms	(* (/ 1 (/ (sin B) (* x 1.0))) (cos B))
7.0ms	(/ 1 (/ (sin B) (* x 1.0)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
37.0ms	(/ (sin B) (* x 1.0))
83.0ms	(* (/ 1 (/ (sin B) (* x 1.0))) (cos B))
48.0ms	(/ 1 (/ (sin B) (* x 1.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	586	1140
1	2698	963
2	5001	905

prune359.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes74.0ms

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	22	10
1	26	10
2	26	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

688.0ms	1682×	body	1280	valid
390.0ms	1499×	body	640	valid
303.0ms	4891×	body	80	valid
132.0ms	725×	body	320	valid
52.0ms	381×	body	160	valid