Details

sample103.0ms

Algorithm

intervals

Results

55.0ms	136×	body	1280	valid
17.0ms	18×	body	2560	valid
16.0ms	64×	body	640	valid
4.0ms	22×	body	320	valid
2.0ms	12×	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: 39.2b

localize9.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (cos (+ x eps)) (cos x))
4.5b	(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))

series71.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (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

prune120.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(fma (sin x) (sin eps) (cos x))
3.1b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite10.0ms

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)))

series223.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* (cos x) (cos eps))
50.0ms	(fma (sin x) (sin eps) (cos x))
131.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify120.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (114.0ms)

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

prune219.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.5b

localize17.0ms

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))
3.1b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite39.0ms

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)))
4.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series295.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos x) (cos eps))
82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms	(* (sin x) (sin eps))
126.0ms	(- (- (* (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

prune319.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (sin x) (sin eps) (cos x))
3.1b	(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))))

series187.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(fma (sin x) (sin eps) (cos x))
134.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify115.0ms

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

prune74.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.5b

regimes196.0ms

Accuracy

86.7% (1.3b remaining)

Error of 15.9b against oracle of 14.5b and baseline of 24.7b

bsearch118.0ms

Steps

Iters	Range		Point
9	7.507640222675324e-06	0.4954286465087044	4.9162524699735606e-05
8	-3.3551436115377164e-08	-2.0275543903092447e-11	-1.1888021786142176e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	25
1	32	25

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.8s	4552×	body	1280	valid
590.0ms	636×	body	2560	valid
464.0ms	1793×	body	640	valid
123.0ms	677×	body	320	valid
36.0ms	271×	body	160	valid
10.0ms	71×	body	80	valid