Details

sample91.0ms

Algorithm

intervals

Results

47.0ms	112×	body	1280	valid
14.0ms	16×	body	2560	valid
14.0ms	57×	body	640	valid
4.0ms	28×	body	320	valid
2.0ms	35×	body	80	valid
1.0ms	8×	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: 36.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (sin (+ x eps)) (sin x))
4.0b	(sin (+ x eps))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 9

Calls

2 calls:

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

series68.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify131.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	111	90
1	261	90
2	825	88
3	3067	88
4	5001	88

prune41.0ms

Filtered

15 candidates to 10 candidates (66.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	3	16

Merged error: 0.3b

Counts

16 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
0.1b	(* (sin eps) (cos x))
0.1b	(* (cos eps) (sin x))
0.8b	(- (* (cos eps) (sin x)) (sin x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 15

Calls

4 calls:

8.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
3.0ms	(* (sin eps) (cos x))
3.0ms	(* (cos eps) (sin x))
4.0ms	(- (* (cos eps) (sin x)) (sin x))

series279.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
47.0ms	(* (sin eps) (cos x))
45.0ms	(* (cos eps) (sin x))
65.0ms	(- (* (cos eps) (sin x)) (sin x))

simplify79.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	210	267
1	664	264
2	2813	247
3	5002	247

prune82.0ms

Filtered

27 candidates to 17 candidates (63.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	23	4	27
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	23	7	30

Merged error: 0.2b

Counts

30 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos eps) (sin x)) (cos eps))
0.3b	(+ (cos eps) 1)
1.0b	(- (* (* (cos eps) (sin x)) (cos eps)) (sin x))
8.3b	(/ (* (sin x) (- (* (* (cos eps) (sin x)) (cos eps)) (sin x))) (* (+ (cos eps) 1) (sin x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-commutative`
4×	`times-frac`
2×	`flip3--` `flip3-+` `associate-r/` `associate-l` `associate-l/` `associate-/r` `associate-/r/` `flip--` `flip-+` `associate-/l/` `associate-/l`
1×	`+-commutative` `sub-neg` `frac-2neg` `clear-num` `div-inv`

Counts

4 → 25

Calls

4 calls:

5.0ms	(* (* (cos eps) (sin x)) (cos eps))
3.0ms	(+ (cos eps) 1)
10.0ms	(- (* (* (cos eps) (sin x)) (cos eps)) (sin x))
13.0ms	(/ (* (sin x) (- (* (* (cos eps) (sin x)) (cos eps)) (sin x))) (* (+ (cos eps) 1) (sin x)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* (cos eps) (sin x)) (cos eps))
10.0ms	(+ (cos eps) 1)
74.0ms	(- (* (* (cos eps) (sin x)) (cos eps)) (sin x))
149.0ms	(/ (* (sin x) (- (* (* (cos eps) (sin x)) (cos eps)) (sin x))) (* (+ (cos eps) 1) (sin x)))

simplify171.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	241	326
1	896	306
2	4670	264
3	5001	264

prune146.0ms

Filtered

37 candidates to 28 candidates (75.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	36	8	44

Merged error: 0.2b

Counts

44 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (pow (cos eps) 2) 1) (/ (sin x) (+ 1 (cos eps))))
0.2b	(pow (cos eps) 2)
0.3b	(+ 1 (cos eps))
1.2b	(- (pow (cos eps) 2) 1)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`frac-times`
5×	`flip3--` `flip--` `unpow2`
4×	`difference-of-sqr-1` `clear-num`
3×	`frac-2neg` `associate-r/` `associate-r*` `sqr-pow`
2×	`flip3-+` `associate-l` `associate-*l/` `sub-1-cos` `associate-/r/` `flip-+`
1×	`+-commutative` `distribute-lft-neg-out` `pow-to-exp` `sub-neg` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 32

Calls

4 calls:

8.0ms	(* (- (pow (cos eps) 2) 1) (/ (sin x) (+ 1 (cos eps))))
1.0ms	(pow (cos eps) 2)
2.0ms	(+ 1 (cos eps))
4.0ms	(- (pow (cos eps) 2) 1)

series183.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (- (pow (cos eps) 2) 1) (/ (sin x) (+ 1 (cos eps))))
18.0ms	(pow (cos eps) 2)
10.0ms	(+ 1 (cos eps))
39.0ms	(- (pow (cos eps) 2) 1)

simplify40.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	253	270
1	1209	268
2	5001	264

prune154.0ms

Filtered

44 candidates to 32 candidates (72.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	45	7	52

Merged error: 0.1b

Counts

52 → 7

regimes71.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	13
1	24	13
2	24	13

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3353×	body	1280	valid
566.0ms	614×	body	2560	valid
448.0ms	1814×	body	640	valid
128.0ms	767×	body	320	valid
54.0ms	1097×	body	80	valid
39.0ms	355×	body	160	valid