Details

sample86.0ms

Algorithm

intervals

Results

39.0ms	70×	body	1280	valid
19.0ms	45×	body	640	valid
11.0ms	140×	body	80	valid
5.0ms	20×	body	320	valid
2.0ms	10×	body	160	valid

simplify12.0ms

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)))
0.1b	(/ 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))
2.0ms	(/ 1.0 (tan B))

series157.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
23.0ms	(/ 1.0 (sin B))
37.0ms	(/ 1.0 (tan B))

simplify59.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (53.0ms)

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

prune228.0ms

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

Counts

3 → 68

Calls

3 calls:

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

series132.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
18.0ms	(/ (cos B) (sin B))

simplify60.0ms

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

prune228.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1 (* x (cos B)))
0.1b	(/ 1.0 (sin B))
0.2b	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
0.2b	(* x (cos B))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

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

series167.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- 1 (* x (cos B)))
18.0ms	(/ 1.0 (sin B))
73.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
39.0ms	(* x (cos B))

simplify63.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	423	840
1	2117	739
2	5002	734

prune297.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1 (* x (cos B)))
0.2b	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))
0.2b	(* x (cos B))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

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

series154.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(- 1 (* x (cos B)))
76.0ms	(/ (* 1.0 (- 1 (* x (cos B)))) (sin B))
40.0ms	(* x (cos B))

simplify41.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	301	437
1	1366	372
2	5001	368

prune169.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	1783×	body	1280	valid
486.0ms	1344×	body	640	valid
420.0ms	4922×	body	80	valid
168.0ms	695×	body	320	valid
65.0ms	356×	body	160	valid