Details

sample87.0ms

Algorithm

intervals

Results

50.0ms	150×	body	1280	valid
13.0ms	16×	body	2560	valid
11.0ms	57×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	8×	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

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: 38.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
3.9b	(cos (+ x eps))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`cos-sum`
2×	`+-commutative` `associate--l-`
1×	`sub-neg` `flip3--` `flip--` `diff-cos`

Counts

2 → 9

Calls

2 calls:

4.0ms	(- (cos (+ x eps)) (cos x))
3.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify106.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 4 (103.0ms)

Iter	Nodes	Cost
0	120	88
1	262	87
2	813	86
3	2865	84
4	5001	82

prune45.0ms

Filtered

15 candidates to 9 candidates (60.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	8	7	15
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	9	7	16

Merged error: 15.0b

Counts

16 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (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))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
8×	`prod-diff`
6×	`associate--l+`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `fma-neg` `flip--`
1×	`associate--l-` `frac-sub` `sub-div`

Counts

4 → 27

Calls

4 calls:

3.0ms	(* (cos x) (cos eps))
7.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
3.0ms	(* (sin x) (sin eps))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series300.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos x) (cos eps))
82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
134.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify62.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	218	337
1	626	325
2	2139	304
3	5002	273

prune109.0ms

Filtered

39 candidates to 25 candidates (64.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	34	5	39
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	36	10	46

Merged error: 14.9b

Counts

46 → 10

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

3×	`fma-udef`
1×	`+-commutative` `associate-+l+` `associate-+r+` `flip3-+` `*-commutative` `flip-+` `sin-mult`

Counts

3 → 8

Calls

3 calls:

1.0ms	(fma (cos eps) (cos x) (- (* (sin x) (sin eps))))
3.0ms	(* (sin x) (sin eps))
2.0ms	(+ (fma (cos eps) (cos x) (- (* (sin x) (sin eps)))) (fma (sin x) (+ (- (sin eps)) (sin eps)) (- (cos x))))

series309.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(fma (cos eps) (cos x) (- (* (sin x) (sin eps))))
44.0ms	(* (sin x) (sin eps))
181.0ms	(+ (fma (cos eps) (cos x) (- (* (sin x) (sin eps)))) (fma (sin x) (+ (- (sin eps)) (sin eps)) (- (cos x))))

simplify45.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	121	191
1	358	188
2	1520	176
3	5001	155

prune83.0ms

Filtered

17 candidates to 12 candidates (70.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	12	5	17
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	14	13	27

Merged error: 14.8b

Counts

27 → 13

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
1.8b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`fma-udef`

Counts

2 → 2

Calls

2 calls:

1.0ms	(fma (sin x) (sin eps) (cos x))
1.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series189.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(fma (sin x) (sin eps) (cos x))
134.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify83.0ms

Algorithm

egg-herbie

Counts

8 → 8

Iterations

Useful iterations: 3 (17.0ms)

Iter	Nodes	Cost
0	64	41
1	165	40
2	494	40
3	2044	38
4	5001	38

prune12.0ms

Filtered

8 candidates to 4 candidates (50.0%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	8	0	8
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	8	13	21

Merged error: 14.8b

Counts

21 → 13

regimes141.0ms

Accuracy

89.7% (1.0b remaining)

Error of 15.2b against oracle of 14.2b and baseline of 24.1b

bsearch110.0ms

Steps

Iters	Range		Point
9	1.9839578581908613e-17	7.414030703724578e-11	7.289861209258843e-11
8	-0.6319501064166059	-3.810242810899289e-05	-3.893780865416545e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	30
1	42	30
2	42	30

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	4530×	body	1280	valid
526.0ms	614×	body	2560	valid
375.0ms	1800×	body	640	valid
103.0ms	697×	body	320	valid
32.0ms	284×	body	160	valid
4.0ms	75×	body	80	valid