Details

sample93.0ms

Algorithm

intervals

Results

51.0ms	154×	body	1280	valid
16.0ms	19×	body	2560	valid
12.0ms	55×	body	640	valid
3.0ms	20×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	4×	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: 40.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (cos (+ x eps)) (cos x))
2.4b	(cos (+ x eps))

rewrite17.0ms

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

series64.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

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

prune120.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.8b

localize18.0ms

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))
2.6b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite26.0ms

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))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series289.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
81.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
47.0ms	(* (sin x) (sin eps))
123.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify47.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (39.0ms)

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

prune322.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.7b

localize20.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
2.6b	(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))))

series195.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(fma (sin x) (sin eps) (cos x))
137.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify120.0ms

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

prune134.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(fma (sin x) (sin eps) (cos x))
2.6b	(+ (* (cos eps) (cos x)) (- (fma (sin x) (sin eps) (cos x))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-log-exp`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u`
2×	`sum-log` `fma-udef`
1×	`+-commutative` `neg-sub0` `associate-+r-` `associate-+r+` `distribute-neg-in` `fma-def` `flip3-+` `unsub-neg` `pow-prod-down` `neg-log` `prod-exp` `cos-mult` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

4.0ms	(* (cos eps) (cos x))
1.0ms	(fma (sin x) (sin eps) (cos x))
6.0ms	(+ (* (cos eps) (cos x)) (- (fma (sin x) (sin eps) (cos x))))

series228.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (cos eps) (cos x))
49.0ms	(fma (sin x) (sin eps) (cos x))
138.0ms	(+ (* (cos eps) (cos x)) (- (fma (sin x) (sin eps) (cos x))))

simplify137.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	241	417
1	939	376
2	4946	369
3	5001	369

prune180.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.6b

regimes159.0ms

Accuracy

85.9% (1.5b remaining)

Error of 15.9b against oracle of 14.5b and baseline of 24.8b

bsearch123.0ms

Steps

Iters	Range		Point
8	8.67121852713505e-19	2.3324237763646973e-15	2.2931718725747495e-15
11	-402.67606408878214	-3.387926217419311e-22	-0.0003904334551807754

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	26
1	35	26

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	4481×	body	1280	valid
543.0ms	634×	body	2560	valid
402.0ms	1845×	body	640	valid
101.0ms	669×	body	320	valid
29.0ms	285×	body	160	valid
5.0ms	86×	body	80	valid