Details

sample330.0ms

Algorithm

intervals

Results

36.0ms	61×	body	1280	valid
13.0ms	39×	body	640	valid
13.0ms	163×	body	80	valid
5.0ms	22×	body	320	valid
2.0ms	11×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

2.0ms	(/ 1.0 (sin B))
0.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (tan B))

series214.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ 1.0 (sin B))
102.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
93.0ms	(/ 1.0 (tan B))

simplify58.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	246	416
1	694	382
2	2127	382
3	5002	377

prune251.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`fma-udef`

Counts

3 → 68

Calls

3 calls:

2.0ms	(/ 1.0 (sin B))
0.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
3.0ms	(/ (cos B) (sin B))

series136.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify62.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	241	480
1	721	438
2	2196	438
3	5001	433

prune240.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-l`
12×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-r` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
3×	`expm1-log1p-u` `prod-exp` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `sub-neg` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv`
1×	`frac-2neg` `associate-*l/` `clear-num`

Counts

3 → 97

Calls

3 calls:

2.0ms	(/ 1.0 (sin B))
3.0ms	(* x (cos B))
14.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

series131.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ 1.0 (sin B))
36.0ms	(* x (cos B))
75.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))

simplify56.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	415	714
1	2101	633
2	5001	629

prune257.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))
0.2b	(* x (cos B))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `expm1-log1p-u` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`flip3--` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `flip--` `div-inv` `associate-/l` `unswap-sqr`

Counts

2 → 45

Calls

2 calls:

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

series114.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))
39.0ms	(* x (cos B))

simplify34.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	248	316
1	1119	266
2	5001	263

prune114.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	9
1	25	9
2	28	9
3	28	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1770×	body	1280	valid
497.0ms	1374×	body	640	valid
403.0ms	5029×	body	80	valid
158.0ms	616×	body	320	valid
58.0ms	339×	body	160	valid