Details

sample91.0ms

Algorithm

intervals

Results

45.0ms	107×	body	1280	valid
16.0ms	18×	body	2560	valid
12.0ms	51×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	10×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 36.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (sin (+ x eps)) (sin x))
3.6b	(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))

series63.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify132.0ms

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

prune38.0ms

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

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin eps) (cos x))
0.1b	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
0.2b	(* (cos eps) (sin x))
1.7b	(- (* (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:

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

series268.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin eps) (cos x))
116.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
43.0ms	(* (cos eps) (sin x))
63.0ms	(- (* (cos eps) (sin x)) (sin x))

simplify81.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (22.0ms)

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

prune79.0ms

Filtered

27 candidates to 17 candidates (63.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	22	5	27
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	24	6	30

Merged error: 0.3b

Counts

30 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos eps) (sin x))
0.5b	(+ (cos eps) 1)
2.0b	(- (* (* (cos eps) (sin x)) (cos eps)) (sin x))
8.6b	(/ (* (sin x) (- (* (* (cos eps) (sin x)) (cos eps)) (sin x))) (* (+ (cos eps) 1) (sin x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 23

Calls

4 calls:

3.0ms	(* (cos eps) (sin x))
3.0ms	(+ (cos eps) 1)
7.0ms	(- (* (* (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)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos eps) (sin x))
10.0ms	(+ (cos eps) 1)
70.0ms	(- (* (* (cos eps) (sin x)) (cos eps)) (sin x))
140.0ms	(/ (* (sin x) (- (* (* (cos eps) (sin x)) (cos eps)) (sin x))) (* (+ (cos eps) 1) (sin x)))

simplify166.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	241	320
1	896	300
2	4670	258
3	5001	258

prune142.0ms

Filtered

35 candidates to 28 candidates (80.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	33	8	41

Merged error: 0.2b

Counts

41 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (cos eps) 1)
1.9b	(- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))
8.6b	(/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (* (+ (pow (cos eps) 2) 1) (sin x)))
8.6b	(/ (* (sin x) (/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (* (+ (pow (cos eps) 2) 1) (sin x)))) (* (+ (cos eps) 1) (sin x)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

34×	`times-frac`
33×	`*-commutative`
21×	`associate-r`
14×	`associate-/l/`
13×	`associate-r/` `associate-/l`
10×	`associate-*l/` `associate-/r/`
6×	`flip3-+` `associate-/r*` `flip-+`
5×	`div-inv`
4×	`clear-num`
3×	`flip3--` `frac-2neg` `flip--`
1×	`+-commutative` `sub-neg` `un-div-inv`

Counts

4 → 66

Calls

4 calls:

3.0ms	(+ (cos eps) 1)
8.0ms	(- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))
16.0ms	(/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (* (+ (pow (cos eps) 2) 1) (sin x)))
22.0ms	(/ (* (sin x) (/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (* (+ (pow (cos eps) 2) 1) (sin x)))) (* (+ (cos eps) 1) (sin x)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (cos eps) 1)
71.0ms	(- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))
164.0ms	(/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (* (+ (pow (cos eps) 2) 1) (sin x)))
206.0ms	(/ (* (sin x) (/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (* (+ (pow (cos eps) 2) 1) (sin x)))) (* (+ (cos eps) 1) (sin x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	513	1241
1	2247	952
2	5001	913

prune335.0ms

Filtered

78 candidates to 67 candidates (85.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	77	9	86

Merged error: 0.2b

Counts

86 → 9

regimes94.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	18
1	29	18

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3322×	body	1280	valid
573.0ms	635×	body	2560	valid
483.0ms	1830×	body	640	valid
131.0ms	767×	body	320	valid
57.0ms	1102×	body	80	valid
38.0ms	344×	body	160	valid