Details

sample92.0ms

Algorithm

intervals

Results

44.0ms	112×	body	1280	valid
18.0ms	21×	body	2560	valid
14.0ms	59×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	35×	body	80	valid
1.0ms	11×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 37.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (sin (+ x eps)) (sin x))
3.8b	(sin (+ 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` `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:

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

series62.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (sin (+ x eps)) (sin x))
23.0ms	(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

prune74.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 14.7b

Counts

31 → 8

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))
2.3b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite27.0ms

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:

6.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (sin x) (cos eps))
4.0ms	(* (cos x) (sin eps))
8.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series278.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
44.0ms	(* (sin x) (cos eps))
41.0ms	(* (cos x) (sin eps))
107.0ms	(- (+ (* (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

prune201.0ms

Filtered

76 candidates to 53 candidates (69.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	74	10	84

Merged error: 0.3b

Counts

84 → 10

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))
1.7b	(- (cos eps) 1)

rewrite26.0ms

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:

8.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
8.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(* (cos x) (sin eps))
4.0ms	(- (cos eps) 1)

series216.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
46.0ms	(* (sin x) (- (cos eps) 1))
44.0ms	(* (cos x) (sin eps))
18.0ms	(- (cos eps) 1)

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

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

prune220.0ms

Filtered

89 candidates to 55 candidates (61.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	86	13	99

Merged error: 0.1b

Counts

99 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.4b	(pow (cos eps) 3)
0.4b	(+ (cos eps) 1)
1.6b	(- (pow (cos eps) 3) 1)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
2.0ms	(pow (cos eps) 3)
4.0ms	(+ (cos eps) 1)
7.0ms	(- (pow (cos eps) 3) 1)

series129.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (sin eps))
27.0ms	(pow (cos eps) 3)
14.0ms	(+ (cos eps) 1)
46.0ms	(- (pow (cos eps) 3) 1)

simplify50.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	317	420
1	1377	378
2	5001	362

prune192.0ms

Filtered

90 candidates to 51 candidates (56.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	90	13	103

Merged error: 0.1b

Counts

103 → 13

regimes112.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	15
1	25	15

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3232×	body	1280	valid
568.0ms	620×	body	2560	valid
472.0ms	1872×	body	640	valid
130.0ms	779×	body	320	valid
56.0ms	1134×	body	80	valid
44.0ms	363×	body	160	valid