Details

sample87.0ms

Algorithm

intervals

Results

47.0ms	146×	body	1280	valid
15.0ms	18×	body	2560	valid
12.0ms	59×	body	640	valid
4.0ms	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))
4.0ms	(cos (+ x eps))

series68.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify111.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 2 (9.0ms)

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

prune189.0ms

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))

rewrite23.0ms

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))

series306.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos x) (cos eps))
81.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
135.0ms	(- (- (* (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	244
1	521	243
2	1783	224
3	5001	217

prune79.0ms

Filtered

29 candidates to 17 candidates (58.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	24	5	29
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	26	9	35

Merged error: 14.8b

Counts

35 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(+ (* (sin eps) (sin x)) (cos x))
0.2b	(* (sin eps) (sin x))
2.8b	(- (* (cos eps) (cos x)) (+ (* (sin eps) (sin x)) (cos x)))

rewrite20.0ms

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

series292.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos eps) (cos x))
62.0ms	(+ (* (sin eps) (sin x)) (cos x))
47.0ms	(* (sin eps) (sin x))
138.0ms	(- (* (cos eps) (cos x)) (+ (* (sin eps) (sin x)) (cos x)))

simplify97.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	214	271
1	771	270
2	3089	259
3	5001	257

prune89.0ms

Filtered

27 candidates to 18 candidates (66.7%)

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: 0.4b

Counts

36 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(- (- (* (cos eps) (cos x)) (cos x)) (* (sin eps) (sin x)))
0.2b	(* (sin eps) (sin x))
1.7b	(- (* (cos eps) (cos x)) (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 eps) (cos x))
7.0ms	(- (- (* (cos eps) (cos x)) (cos x)) (* (sin eps) (sin x)))
3.0ms	(* (sin eps) (sin x))
5.0ms	(- (* (cos eps) (cos x)) (cos x))

series293.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos eps) (cos x))
130.0ms	(- (- (* (cos eps) (cos x)) (cos x)) (* (sin eps) (sin x)))
46.0ms	(* (sin eps) (sin x))
75.0ms	(- (* (cos eps) (cos x)) (cos x))

simplify73.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	184	273
1	580	267
2	2423	250
3	5002	250

prune64.0ms

Filtered

29 candidates to 18 candidates (62.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	24	5	29
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	26	12	38

Merged error: 0.3b

Counts

38 → 12

regimes139.0ms

Accuracy

91.5% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 6.3b

bsearch117.0ms

Steps

Iters	Range		Point
8	3.88064682879673e-06	0.018000635171863108	5.23681108699865e-06
9	-1.485944467815708e-07	-6.8508537417624476e-15	-1.4576344074687237e-07

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	56
1	44	56
2	44	56

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4480×	body	1280	valid
541.0ms	635×	body	2560	valid
402.0ms	1845×	body	640	valid
115.0ms	673×	body	320	valid
28.0ms	289×	body	160	valid
4.0ms	78×	body	80	valid