Details

sample121.0ms

Algorithm

intervals

Results

57.0ms	128×	body	1280	valid
30.0ms	31×	body	2560	valid
18.0ms	63×	body	640	valid
4.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
4.6b	(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:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series19.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

simplify71.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (67.0ms)

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

prune257.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.6b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite9.0ms

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:

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

series43.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(* (cos x) (cos eps))
12.0ms	(fma (sin x) (sin eps) (cos x))
23.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify112.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (107.0ms)

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

prune508.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.4b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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

2 → 20

Calls

2 calls:

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

series36.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(fma (sin x) (sin eps) (cos x))
24.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify112.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	87	209
1	240	182
2	795	182
3	3587	180
4	5001	180

prune322.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.4b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `sin-mult` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

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

series43.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(* (sin x) (sin eps))
11.0ms	(+ (* (sin x) (sin eps)) (cos x))
24.0ms	(fma (cos eps) (cos x) (- (+ (* (sin x) (sin eps)) (cos x))))

simplify75.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	205	378
1	645	339
2	2519	338
3	5001	336

prune383.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 15.4b

regimes442.0ms

Accuracy

86.2% (1.3b remaining)

Error of 16.3b against oracle of 14.9b and baseline of 24.5b

bsearch90.0ms

Steps

Iters	Range		Point
10	9.316647860064626e-18	0.006665254470786589	4.819151863418274e-08
6	-1.8496456666423901e-16	-1.9909943074331788e-17	-1.8216181721535518e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	26
1	43	26
2	43	26

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.0s	4473×	body	1280	valid
661.0ms	667×	body	2560	valid
551.0ms	1820×	body	640	valid
141.0ms	658×	body	320	valid
52.0ms	306×	body	160	valid
10.0ms	76×	body	80	valid