Details

sample95.0ms

Algorithm

intervals

Results

50.0ms	112×	body	1280	valid
15.0ms	16×	body	2560	valid
13.0ms	57×	body	640	valid
5.0ms	28×	body	320	valid
2.0ms	35×	body	80	valid
1.0ms	8×	body	160	valid

simplify6.0ms

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))

rewrite8.0ms

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

series55.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify136.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 4 (134.0ms)

Iter	Nodes	Cost
0	117	90
1	282	88
2	919	87
3	3429	86
4	5001	85

prune37.0ms

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

localize13.0ms

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

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

Counts

4 → 19

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

series257.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
42.0ms	(* (sin eps) (cos x))
44.0ms	(* (cos eps) (sin x))
60.0ms	(- (* (cos eps) (sin x)) (sin x))

simplify80.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	227	262
1	751	252
2	3222	235
3	5001	235

prune95.0ms

Filtered

31 candidates to 22 candidates (71.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	28	6	34

Merged error: 0.2b

Counts

34 → 6

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

2×	`fma-def` `*-commutative` `fma-udef`
1×	`+-commutative` `associate-+r+` `flip3-+` `sin-cos-mult` `flip-+`

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (* (sin eps) (cos x)) (fma (cos eps) (sin x) (- (sin x))))
3.0ms	(* (sin eps) (cos x))
1.0ms	(fma (cos eps) (sin x) (- (sin x)))

series225.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(+ (* (sin eps) (cos x)) (fma (cos eps) (sin x) (- (sin x))))
47.0ms	(* (sin eps) (cos x))
62.0ms	(fma (cos eps) (sin x) (- (sin x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	127	124
1	364	120
2	1360	118
3	5002	117

prune64.0ms

Filtered

18 candidates to 14 candidates (77.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	18	6	24

Merged error: 0.2b

Counts

24 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-commutative`
4×	`fma-neg` `associate-l`
2×	`flip3--` `associate-r/` `flip--` `associate-/l/` `associate-/l`
1×	`sub-neg` `frac-2neg` `clear-num` `fma-udef` `div-inv`

Counts

4 → 19

Calls

4 calls:

4.0ms	(* (* (cos eps) (sin x)) (cos eps))
1.0ms	(fma (cos eps) (sin x) (sin x))
7.0ms	(- (* (* (cos eps) (sin x)) (cos eps)) (sin x))
10.0ms	(/ (* (sin x) (- (* (* (cos eps) (sin x)) (cos eps)) (sin x))) (fma (cos eps) (sin x) (sin x)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* (cos eps) (sin x)) (cos eps))
75.0ms	(fma (cos eps) (sin x) (sin x))
71.0ms	(- (* (* (cos eps) (sin x)) (cos eps)) (sin x))
255.0ms	(/ (* (sin x) (- (* (* (cos eps) (sin x)) (cos eps)) (sin x))) (fma (cos eps) (sin x) (sin x)))

simplify81.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	172	238
1	603	231
2	2368	214
3	5002	208

prune96.0ms

Filtered

31 candidates to 22 candidates (71.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	29	8	37

Merged error: 0.2b

Counts

37 → 8

regimes78.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	12	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3353×	body	1280	valid
553.0ms	614×	body	2560	valid
424.0ms	1814×	body	640	valid
122.0ms	767×	body	320	valid
61.0ms	1097×	body	80	valid
44.0ms	355×	body	160	valid