Details

sample87.0ms

Algorithm

intervals

Results

47.0ms	146×	body	1280	valid
15.0ms	18×	body	2560	valid
12.0ms	59×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	4×	body	80	valid

simplify10.0ms

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: 39.0b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (cos (+ x eps)) (cos x))
3.5b	(cos (+ x eps))

rewrite8.0ms

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))

series65.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify109.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 4 (107.0ms)

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

prune46.0ms

Filtered

15 candidates to 9 candidates (60.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	9	6	15
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	10	6	16

Merged error: 14.9b

Counts

16 → 6

localize15.0ms

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))
2.8b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite24.0ms

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))

series295.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos x) (cos eps))
80.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
130.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify58.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (54.0ms)

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

prune123.0ms

Filtered

39 candidates to 25 candidates (64.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	30	9	39
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	34	11	45

Merged error: 14.7b

Counts

45 → 11

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (cos eps) (cos x) (- (* (sin eps) (sin x))))
0.2b	(* (sin eps) (sin x))
2.8b	(+ (fma (cos eps) (cos x) (- (* (sin eps) (sin x)))) (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 eps) (sin x))))
3.0ms	(* (sin eps) (sin x))
2.0ms	(+ (fma (cos eps) (cos x) (- (* (sin eps) (sin x)))) (fma (sin x) (+ (- (sin eps)) (sin eps)) (- (cos x))))

series296.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(fma (cos eps) (cos x) (- (* (sin eps) (sin x))))
47.0ms	(* (sin eps) (sin x))
168.0ms	(+ (fma (cos eps) (cos x) (- (* (sin eps) (sin x)))) (fma (sin x) (+ (- (sin eps)) (sin eps)) (- (cos x))))

simplify46.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	124	191
1	365	188
2	1525	176
3	5001	155

prune89.0ms

Filtered

17 candidates to 12 candidates (70.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	13	4	17
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	16	12	28

Merged error: 14.7b

Counts

28 → 12

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
2.8b	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite2.0ms

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))))

series188.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(fma (sin x) (sin eps) (cos x))
138.0ms	(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify86.0ms

Algorithm

egg-herbie

Counts

8 → 8

Iterations

Useful iterations: 3 (18.0ms)

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

prune9.0ms

Filtered

8 candidates to 3 candidates (37.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	7	1	8
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	7	13	20

Merged error: 14.7b

Counts

20 → 13

regimes152.0ms

Accuracy

84.5% (1.5b remaining)

Error of 16.0b against oracle of 14.6b and baseline of 24.2b

bsearch114.0ms

Steps

Iters	Range		Point
8	3.88064682879673e-06	0.018000635171863108	4.6943453837178825e-06
9	-2.981750332052767e-33	-1.3727521311823731e-39	-2.9500525747086803e-33

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	4480×	body	1280	valid
543.0ms	635×	body	2560	valid
385.0ms	1845×	body	640	valid
93.0ms	673×	body	320	valid
27.0ms	289×	body	160	valid
4.0ms	78×	body	80	valid