Details

sample84.0ms

Algorithm

intervals

Results

37.0ms	59×	body	1280	valid
18.0ms	53×	body	640	valid
11.0ms	138×	body	80	valid
6.0ms	25×	body	320	valid
2.0ms	10×	body	160	valid

simplify11.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite7.0ms

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:

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

series154.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
24.0ms	(/ 1.0 (sin B))
34.0ms	(/ 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

prune242.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

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:

3.0ms	(* x (cos B))
17.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
2.0ms	(/ 1.0 (sin B))

series132.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* x (cos B))
77.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
18.0ms	(/ 1.0 (sin 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

prune254.0ms

Pruning

9 alts after pruning (9 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	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))

rewrite13.0ms

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:

3.0ms	(* x (cos B))
8.0ms	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))

series112.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* x (cos B))
77.0ms	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))

simplify34.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	248	316
1	1125	266
2	5001	263

prune134.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin B) (- 1 (* x (cos B))))
0.1b	(* x (cos B))
0.2b	(/ 1.0 (/ (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×	`associate-/r*`
12×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r/`
6×	`div-inv` `associate-/l*`
5×	`pow1` `flip3--` `flip--`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 131

Calls

3 calls:

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

series161.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (sin B) (- 1 (* x (cos B))))
35.0ms	(* x (cos B))
75.0ms	(/ 1.0 (/ (sin B) (- 1 (* x (cos B)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	558	1439
1	2756	1360
2	5001	1353

prune367.0ms

Pruning

9 alts after pruning (8 fresh and 1 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

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	6
1	13	6

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	1737×	body	1280	valid
505.0ms	1420×	body	640	valid
382.0ms	4887×	body	80	valid
164.0ms	704×	body	320	valid
59.0ms	361×	body	160	valid