Details

sample100.0ms

Algorithm

intervals

Results

51.0ms	149×	body	1280	valid
21.0ms	24×	body	2560	valid
16.0ms	62×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	5×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (cos (+ x eps)) (cos x))
3.7b	(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))

series75.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

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

prune125.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
1.9b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`prod-diff` `add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate--l+` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
10.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series319.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos x) (cos eps))
88.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
46.0ms	(* (sin x) (sin eps))
139.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	381	988
1	1342	837
2	5002	822

prune315.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.8b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
1.9b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite2.0ms

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:

1.0ms	(fma (sin x) (sin eps) (cos x))
1.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series200.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(fma (sin x) (sin eps) (cos x))
147.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify119.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (26.0ms)

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

prune145.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
0.1b	(log1p (expm1 (fma (sin x) (sin eps) (cos x))))
0.6b	(expm1 (fma (sin x) (sin eps) (cos x)))
5.1b	(fma (cos eps) (cos x) (- (log1p (expm1 (fma (sin x) (sin eps) (cos x))))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 42

Calls

4 calls:

1.0ms	(fma (sin x) (sin eps) (cos x))
1.0ms	(log1p (expm1 (fma (sin x) (sin eps) (cos x))))
1.0ms	(expm1 (fma (sin x) (sin eps) (cos x)))
1.0ms	(fma (cos eps) (cos x) (- (log1p (expm1 (fma (sin x) (sin eps) (cos x))))))

series425.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(fma (sin x) (sin eps) (cos x))
93.0ms	(log1p (expm1 (fma (sin x) (sin eps) (cos x))))
88.0ms	(expm1 (fma (sin x) (sin eps) (cos x)))
189.0ms	(fma (cos eps) (cos x) (- (log1p (expm1 (fma (sin x) (sin eps) (cos x))))))

simplify44.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	143	404
1	377	348
2	1274	346
3	5001	343

prune172.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 16.7b

regimes195.0ms

Accuracy

86.2% (1.4b remaining)

Error of 16.3b against oracle of 15.0b and baseline of 24.9b

bsearch137.0ms

Steps

Iters	Range		Point
9	1.2358748968334836e-07	0.23288488004633429	1.8711149652135092e-06
10	-9.963366173383092e-17	-1.5200352594837407e-30	-9.839040800040512e-17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	15
1	30	15

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4491×	body	1280	valid
596.0ms	676×	body	2560	valid
407.0ms	1793×	body	640	valid
120.0ms	680×	body	320	valid
32.0ms	296×	body	160	valid
4.0ms	64×	body	80	valid