Details

sample89.0ms

Algorithm

intervals

Results

49.0ms	152×	body	1280	valid
17.0ms	20×	body	2560	valid
8.0ms	41×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	6×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
1.8b	(cos (+ x eps))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

8.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series75.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(- (cos (+ x eps)) (cos x))
23.0ms	(cos (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	192	385
1	523	285
2	2519	275
3	5001	220

prune120.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
0.1b	(* (cos x) (cos eps))
2.3b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `cos-mult` `*-commutative` `flip--` `cbrt-unprod` `associate--r+` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

0.0ms	(fma (sin x) (sin eps) (cos x))
4.0ms	(* (cos x) (cos eps))
4.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(fma (sin x) (sin eps) (cos x))
40.0ms	(* (cos x) (cos eps))
133.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify120.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	235	486
1	832	409
2	4494	406
3	5001	404

prune217.0ms

Filtered

59 candidates to 43 candidates (72.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.6b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
0.1b	(fma (sin x) (sin eps) (cos x))
2.2b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

3 → 30

Calls

3 calls:

0.0ms	(fma (sin x) (sin eps) (cos x))
0.0ms	(fma (sin x) (sin eps) (cos x))
0.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series243.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(fma (sin x) (sin eps) (cos x))
54.0ms	(fma (sin x) (sin eps) (cos x))
136.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify116.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	87	285
1	240	248
2	795	248
3	3587	245
4	5001	245

prune198.0ms

Filtered

39 candidates to 33 candidates (84.6%)

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 15.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
2.3b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`prod-diff` `cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `fma-def` `fma-neg` `flip--` `sin-mult` `associate--r+`

Counts

4 → 78

Calls

4 calls:

4.0ms	(+ (* (sin x) (sin eps)) (cos x))
4.0ms	(* (cos x) (cos eps))
4.0ms	(* (sin x) (sin eps))
12.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (* (sin x) (sin eps)) (cos x))
43.0ms	(* (cos x) (cos eps))
46.0ms	(* (sin x) (sin eps))
132.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	389	759
1	1561	655
2	5001	644

prune231.0ms

Filtered

90 candidates to 64 candidates (71.1%)

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 15.5b

regimes193.0ms

Accuracy

87.3% (1.3b remaining)

Error of 15.7b against oracle of 14.4b and baseline of 24.8b

bsearch132.0ms

Steps

Iters	Range		Point
9	0.0004320794088804456	4717.815806685034	0.000437654115253876
9	-8.316448984380752e-05	-4.3283440329487994e-10	-1.5330496627903165e-07

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	29
1	40	29

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	4449×	body	1280	valid
596.0ms	693×	body	2560	valid
391.0ms	1793×	body	640	valid
91.0ms	679×	body	320	valid
29.0ms	309×	body	160	valid
4.0ms	77×	body	80	valid