Details

sample88.0ms

Algorithm

intervals

Results

50.0ms	137×	body	1280	valid
14.0ms	71×	body	640	valid
11.0ms	12×	body	2560	valid
3.0ms	21×	body	320	valid
1.0ms	13×	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: 41.8b

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (cos (+ x eps)) (cos x))
3.6b	(cos (+ x eps))

rewrite25.0ms

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:

15.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series61.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

simplify72.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (68.0ms)

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

prune161.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.5b

localize14.0ms

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))
3.3b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite106.0ms

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:

11.0ms	(* (cos x) (cos eps))
17.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
12.0ms	(* (sin x) (sin eps))
64.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series257.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
67.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
43.0ms	(* (sin x) (sin eps))
110.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify46.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (38.0ms)

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

prune533.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

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))
3.4b	(+ (* (cos x) (cos eps)) (- (fma (sin x) (sin eps) (cos x))))

rewrite23.0ms

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:

10.0ms	(* (cos x) (cos eps))
0.0ms	(fma (sin x) (sin eps) (cos x))
12.0ms	(+ (* (cos x) (cos eps)) (- (fma (sin x) (sin eps) (cos x))))

series199.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* (cos x) (cos eps))
44.0ms	(fma (sin x) (sin eps) (cos x))
116.0ms	(+ (* (cos x) (cos eps)) (- (fma (sin x) (sin eps) (cos x))))

simplify129.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	246	418
1	954	377
2	4899	369
3	5001	369

prune380.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
0.2b	(log1p (expm1 (fma (sin x) (sin eps) (cos x))))
0.7b	(expm1 (fma (sin x) (sin eps) (cos x)))
4.6b	(+ (* (cos x) (cos eps)) (- (log1p (expm1 (fma (sin x) (sin eps) (cos x))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`sum-log`
2×	`log1p-udef` `neg-log`
1×	`+-commutative` `neg-sub0` `associate-+r-` `expm1-log1p` `fma-def` `flip3-+` `log1p-expm1` `unsub-neg` `flip-+` `fma-udef` `expm1-udef`

Counts

4 → 51

Calls

4 calls:

0.0ms	(fma (sin x) (sin eps) (cos x))
0.0ms	(log1p (expm1 (fma (sin x) (sin eps) (cos x))))
0.0ms	(expm1 (fma (sin x) (sin eps) (cos x)))
12.0ms	(+ (* (cos x) (cos eps)) (- (log1p (expm1 (fma (sin x) (sin eps) (cos x))))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(fma (sin x) (sin eps) (cos x))
79.0ms	(log1p (expm1 (fma (sin x) (sin eps) (cos x))))
74.0ms	(expm1 (fma (sin x) (sin eps) (cos x)))
156.0ms	(+ (* (cos x) (cos eps)) (- (log1p (expm1 (fma (sin x) (sin eps) (cos x))))))

simplify101.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	237	523
1	859	444
2	4001	435
3	5001	431

prune295.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.3b

regimes317.0ms

Accuracy

84.3% (1.6b remaining)

Error of 15.8b against oracle of 14.2b and baseline of 24.5b

bsearch138.0ms

Steps

Iters	Range		Point
8	5.9790464235888496e-05	0.05496260612073811	6.037456528482188e-05
10	-415.9104570848854	-2.5612855498029964e-09	-1.7795876728842304e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	28
1	38	28

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.8s	4466×	body	1280	valid
519.0ms	609×	body	2560	valid
403.0ms	1890×	body	640	valid
95.0ms	651×	body	320	valid
35.0ms	303×	body	160	valid
4.0ms	81×	body	80	valid