Details

sample88.0ms

Algorithm

intervals

Results

38.0ms	97×	body	1280	valid
19.0ms	22×	body	2560	valid
15.0ms	68×	body	640	valid
3.0ms	21×	body	320	valid
2.0ms	39×	body	80	valid
1.0ms	9×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 38.3b

localize12.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
2.9b	(sin (+ x eps))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

48.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series64.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

simplify141.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	133	175
1	301	166
2	937	164
3	3445	164
4	5001	164

prune77.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
2.0b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite90.0ms

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`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate--l+` `sin-cos-mult` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

15.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
11.0ms	(* (sin x) (cos eps))
14.0ms	(* (cos x) (sin eps))
48.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series301.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
44.0ms	(* (sin x) (cos eps))
49.0ms	(* (cos x) (sin eps))
115.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	308	589
1	1168	555
2	5001	543

prune230.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (- (cos eps) 1))
0.2b	(* (cos x) (sin eps))
1.9b	(- (cos eps) 1)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-r`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `difference-of-squares`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

21.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
28.0ms	(* (sin x) (- (cos eps) 1))
12.0ms	(* (cos x) (sin eps))
7.0ms	(- (cos eps) 1)

series232.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
47.0ms	(* (sin x) (- (cos eps) 1))
49.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify51.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5001	499

prune269.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.2b	(pow (* (sin x) (- (cos eps) 1)) 3)
1.9b	(- (cos eps) 1)
11.7b	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`add-log-exp`
4×	`cube-div` `associate-*r/`
3×	`pow-unpow` `flip3--` `associate-r` `associate-l` `flip--`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow1/3` `diff-log` `difference-of-sqr-1` `*-commutative` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

11.0ms	(* (cos x) (sin eps))
17.0ms	(pow (* (sin x) (- (cos eps) 1)) 3)
6.0ms	(- (cos eps) 1)
6.0ms	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

series249.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (sin eps))
133.0ms	(pow (* (sin x) (- (cos eps) 1)) 3)
24.0ms	(- (cos eps) 1)
47.0ms	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	334	524
1	1422	478
2	5001	476

prune263.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes105.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	19
1	27	19
2	27	19

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	3230×	body	1280	valid
584.0ms	653×	body	2560	valid
457.0ms	1897×	body	640	valid
127.0ms	778×	body	320	valid
57.0ms	1118×	body	80	valid
33.0ms	324×	body	160	valid