Details

sample93.0ms

Algorithm

intervals

Results

47.0ms	110×	body	1280	valid
16.0ms	19×	body	2560	valid
13.0ms	57×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	39×	body	80	valid
1.0ms	13×	body	160	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: 34.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (sin (+ x eps)) (sin x))
3.7b	(sin (+ x eps))

rewrite52.0ms

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:

41.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series63.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify138.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

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

prune86.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
1.7b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite86.0ms

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:

14.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
11.0ms	(* (sin x) (cos eps))
11.0ms	(* (cos x) (sin eps))
49.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series312.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
46.0ms	(* (sin x) (cos eps))
51.0ms	(* (cos x) (sin eps))
118.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (34.0ms)

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

prune229.0ms

Pruning

12 alts after pruning (12 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)))
0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (- (cos eps) 1))
1.8b	(- (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)))
11.0ms	(* (cos x) (sin eps))
29.0ms	(* (sin x) (- (cos eps) 1))
7.0ms	(- (cos eps) 1)

series250.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
53.0ms	(* (cos x) (sin eps))
50.0ms	(* (sin x) (- (cos eps) 1))
25.0ms	(- (cos eps) 1)

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

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

prune255.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (cbrt (pow (- (cos eps) 1) 3)))
0.4b	(cbrt (pow (- (cos eps) 1) 3))
0.4b	(pow (- (cos eps) 1) 3)
1.8b	(- (cos eps) 1)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

47.0ms	(* (sin x) (cbrt (pow (- (cos eps) 1) 3)))
13.0ms	(cbrt (pow (- (cos eps) 1) 3))
10.0ms	(pow (- (cos eps) 1) 3)
7.0ms	(- (cos eps) 1)

series146.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (sin x) (cbrt (pow (- (cos eps) 1) 3)))
20.0ms	(cbrt (pow (- (cos eps) 1) 3))
47.0ms	(pow (- (cos eps) 1) 3)
25.0ms	(- (cos eps) 1)

simplify49.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	328	760
1	1453	712
2	5002	690

prune307.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes102.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	29	13
2	32	13
3	32	13

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	3285×	body	1280	valid
545.0ms	615×	body	2560	valid
442.0ms	1876×	body	640	valid
281.0ms	1095×	body	80	valid
129.0ms	770×	body	320	valid
36.0ms	359×	body	160	valid