Details

sample96.0ms

Algorithm

intervals

Results

43.0ms	100×	body	1280	valid
20.0ms	22×	body	2560	valid
15.0ms	58×	body	640	valid
6.0ms	32×	body	320	valid
2.0ms	38×	body	80	valid
1.0ms	6×	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: 36.2b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (sin (+ x eps)) (sin x))
2.9b	(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))

series61.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
17.0ms	(sin (+ x eps))

simplify135.0ms

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

prune79.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 14.5b

Counts

31 → 7

localize14.0ms

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))
1.4b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite25.0ms

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)))
5.0ms	(* (sin x) (cos eps))
4.0ms	(* (cos x) (sin eps))
9.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series283.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
44.0ms	(* (sin x) (cos eps))
43.0ms	(* (cos x) (sin eps))
110.0ms	(- (+ (* (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

prune221.0ms

Filtered

76 candidates to 54 candidates (71.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 0.3b

Counts

83 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (- (cos eps) 1))
0.2b	(* (cos x) (sin eps))
1.8b	(- (cos eps) 1)

rewrite27.0ms

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:

9.0ms	(+ (* (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:

106.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
47.0ms	(* (sin x) (- (cos eps) 1))
42.0ms	(* (cos x) (sin eps))
21.0ms	(- (cos eps) 1)

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

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

prune247.0ms

Filtered

89 candidates to 56 candidates (62.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	78	11	89
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	86	14	100

Merged error: 0.1b

Counts

100 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.3b	(cbrt (pow (- (cos eps) 1) 3))
0.4b	(pow (- (cos eps) 1) 3)
1.8b	(- (cos eps) 1)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
20×	`cbrt-prod`
14×	`unpow-prod-down` `cube-prod`
12×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `associate-r` `associate-l` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
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` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
5.0ms	(cbrt (pow (- (cos eps) 1) 3))
5.0ms	(pow (- (cos eps) 1) 3)
4.0ms	(- (cos eps) 1)

series126.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (sin eps))
18.0ms	(cbrt (pow (- (cos eps) 1) 3))
47.0ms	(pow (- (cos eps) 1) 3)
19.0ms	(- (cos eps) 1)

simplify47.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	333	552
1	1340	514
2	5001	506

prune203.0ms

Filtered

110 candidates to 53 candidates (48.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	110	14	124

Merged error: 0.1b

Counts

124 → 14

regimes127.0ms

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	19	10
1	19	10

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	3276×	body	1280	valid
613.0ms	641×	body	2560	valid
501.0ms	1829×	body	640	valid
150.0ms	803×	body	320	valid
71.0ms	1114×	body	80	valid
42.0ms	337×	body	160	valid