Details

sample97.0ms

Algorithm

intervals

Results

56.0ms	147×	body	1280	valid
14.0ms	64×	body	640	valid
13.0ms	15×	body	2560	valid
4.0ms	17×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	3×	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: 37.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite14.0ms

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:

8.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (71.0ms)

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

prune117.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.5b

localize15.0ms

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))
1.5b	(- (- (* (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))
24.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series299.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (cos eps))
83.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
129.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify50.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (41.0ms)

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

prune307.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.4b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
1.5b	(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))))

series192.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(fma (sin x) (sin eps) (cos x))
141.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify117.0ms

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

prune162.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
1.5b	(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)) (cos x))
4.0ms	(* (sin x) (sin eps))
0.0ms	(fma (cos eps) (cos x) (- (+ (* (sin x) (sin eps)) (cos x))))

series239.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(+ (* (sin x) (sin eps)) (cos x))
44.0ms	(* (sin x) (sin eps))
140.0ms	(fma (cos eps) (cos x) (- (+ (* (sin x) (sin eps)) (cos x))))

simplify79.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (74.0ms)

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

prune188.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.3b

regimes186.0ms

Accuracy

76.9% (2.3b remaining)

Error of 16.5b against oracle of 14.1b and baseline of 24.2b

bsearch164.0ms

Steps

Iters	Range		Point
9	2.7116842415582216e-61	3.3093313890471513e-56	3.2757173728301646e-56
11	-772.3369502403921	-2.4819713468358348e-26	-1.0538197704106062e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	37
1	45	37

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4459×	body	1280	valid
577.0ms	656×	body	2560	valid
427.0ms	1856×	body	640	valid
117.0ms	691×	body	320	valid
30.0ms	263×	body	160	valid
5.0ms	75×	body	80	valid