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

simplify11.0ms

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))

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))

series67.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify99.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	112	91
1	237	91
2	715	88
3	2494	88
4	5001	88

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))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `associate--l+` `*-commutative` `flip--`
1×	`associate--l-` `frac-sub` `sub-div`

Counts

4 → 17

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))

series313.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos x) (cos eps))
86.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
46.0ms	(* (sin x) (sin eps))
136.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify53.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	187	243
1	521	242
2	1783	224
3	5001	217

prune81.0ms

Filtered

29 candidates to 17 candidates (58.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	23	6	29
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	27	9	36

Merged error: 14.9b

Counts

36 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

3×	`cos-mult`
2×	`+-commutative` `flip3-+` `*-commutative` `frac-sub` `flip-+` `associate--r+`
1×	`sub-neg` `flip3--` `flip--` `sin-mult`

Counts

4 → 15

Calls

4 calls:

3.0ms	(* (cos x) (cos eps))
5.0ms	(+ (* (sin x) (sin eps)) (cos x))
3.0ms	(* (sin x) (sin eps))
9.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (cos eps))
58.0ms	(+ (* (sin x) (sin eps)) (cos x))
47.0ms	(* (sin x) (sin eps))
140.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	215	272
1	687	271
2	2697	259
3	5002	259

prune84.0ms

Filtered

27 candidates to 17 candidates (63.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	23	4	27
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	27	9	36

Merged error: 0.2b

Counts

36 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (- (* (cos x) (cos eps)) (cos x)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
1.3b	(- (* (cos x) (cos eps)) (cos x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

3×	`sub-neg` `flip3--` `flip--` `sin-mult`
2×	`associate--l+` `*-commutative` `frac-sub`
1×	`associate--l-` `cos-mult`

Counts

4 → 17

Calls

4 calls:

3.0ms	(* (cos x) (cos eps))
7.0ms	(- (- (* (cos x) (cos eps)) (cos x)) (* (sin x) (sin eps)))
3.0ms	(* (sin x) (sin eps))
5.0ms	(- (* (cos x) (cos eps)) (cos x))

series301.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (cos eps))
128.0ms	(- (- (* (cos x) (cos eps)) (cos x)) (* (sin x) (sin eps)))
49.0ms	(* (sin x) (sin eps))
80.0ms	(- (* (cos x) (cos eps)) (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	185	276
1	560	270
2	2232	250
3	5002	249

prune62.0ms

Filtered

29 candidates to 18 candidates (62.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	25	4	29
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	29	9	38

Merged error: 0.2b

Counts

38 → 9

regimes114.0ms

Accuracy

92.7% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 6.3b

bsearch135.0ms

Steps

Iters	Range		Point
11	7.414030703724578e-11	4524963932.878733	1.1486778670333402e-05
8	-0.6319501064166059	-3.810242810899289e-05	-3.893780865416545e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	60
1	42	60

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	4530×	body	1280	valid
547.0ms	614×	body	2560	valid
366.0ms	1800×	body	640	valid
96.0ms	697×	body	320	valid
27.0ms	284×	body	160	valid
4.0ms	75×	body	80	valid