Details

sample89.0ms

Algorithm

intervals

Results

46.0ms	150×	body	1280	valid
21.0ms	25×	body	2560	valid
11.0ms	57×	body	640	valid
2.0ms	18×	body	320	valid
0.0ms	4×	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: 35.9b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

6.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series68.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify107.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune87.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
1.8b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

3.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (sin x) (sin eps))
19.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series290.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
126.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify122.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4487	583
3	5002	583

prune235.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (- (* (sin x) (sin eps))) (cos x))
0.2b	(* (sin x) (sin eps))
1.8b	(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-log-exp`
14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`diff-log`
3×	`sum-log` `cos-mult`
2×	`sub-neg` `associate-+r+` `flip3--` `pow-prod-down` `neg-log` `frac-add` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate--l-` `neg-sub0` `associate-+r-` `flip3-+` `flip-+` `sin-mult` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

3.0ms	(* (cos x) (cos eps))
5.0ms	(- (- (* (sin x) (sin eps))) (cos x))
4.0ms	(* (sin x) (sin eps))
13.0ms	(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos x) (cos eps))
61.0ms	(- (- (* (sin x) (sin eps))) (cos x))
50.0ms	(* (sin x) (sin eps))
127.0ms	(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	362	707
1	1473	662
2	5001	640

prune277.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(- (- (* (sin x) (sin eps))) (cos x))
0.2b	(* (sin x) (sin eps))
1.8b	(+ (* (cos eps) (cos x)) (- (- (* (sin x) (sin eps))) (cos x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-log-exp`
14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`diff-log`
3×	`sum-log` `cos-mult`
2×	`sub-neg` `associate-+r+` `flip3--` `pow-prod-down` `neg-log` `frac-add` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate--l-` `neg-sub0` `associate-+r-` `flip3-+` `flip-+` `sin-mult` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

3.0ms	(* (cos eps) (cos x))
6.0ms	(- (- (* (sin x) (sin eps))) (cos x))
4.0ms	(* (sin x) (sin eps))
13.0ms	(+ (* (cos eps) (cos x)) (- (- (* (sin x) (sin eps))) (cos x)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos eps) (cos x))
59.0ms	(- (- (* (sin x) (sin eps))) (cos x))
44.0ms	(* (sin x) (sin eps))
137.0ms	(+ (* (cos eps) (cos x)) (- (- (* (sin x) (sin eps))) (cos x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	363	706
1	1451	657
2	5001	642

prune228.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 11.3b

regimes207.0ms

Accuracy

84.1% (1.6b remaining)

Error of 15.9b against oracle of 14.2b and baseline of 24.5b

bsearch111.0ms

Steps

Iters	Range		Point
9	1.6022175866244216e-06	1831.6130620084434	2.811292656550888e-06
7	-5.203951087402867e-31	-1.1349252923434323e-32	-5.119551648445698e-31

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	17
1	44	17
2	44	17

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	4507×	body	1280	valid
592.0ms	1835×	body	640	valid
525.0ms	618×	body	2560	valid
95.0ms	646×	body	320	valid
29.0ms	305×	body	160	valid
4.0ms	89×	body	80	valid