Details

sample141.0ms

Algorithm

intervals

Results

71.0ms	52×	body	2560	valid
42.0ms	89×	body	1280	valid
14.0ms	62×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	11×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	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: 31.4b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.2b	(- 1.0 (cos x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3--` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `div-sub` `clear-num` `div-inv`

Counts

2 → 10

Calls

2 calls:

4.0ms	(/ (- 1.0 (cos x)) (sin x))
2.0ms	(- 1.0 (cos x))

series57.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify147.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	124	74
1	332	72
2	964	72
3	3956	71
4	5001	71

prune46.0ms

Filtered

16 candidates to 11 candidates (68.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	9	7	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	9	8	17

Merged error: 0.2b

Counts

17 → 8

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`fma-udef`

Counts

1 → 1

Calls

1 calls:

1.0ms

(fma 1/240 (pow x 5) (* 1/2 x))

series117.0ms

Counts

1 → 3

Calls

1 calls:

116.0ms

(fma 1/240 (pow x 5) (* 1/2 x))

simplify111.0ms

Algorithm

egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	11
1	28	11
2	59	11
3	152	11
4	691	11
5	2399	11
6	5001	11

prune18.0ms

Filtered

4 candidates to 2 candidates (50.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	4	8	12

Merged error: 0.2b

Counts

12 → 8

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
2.2b	(- 1.0 (cos x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`associate-/r/`
4×	`clear-num`
3×	`flip3--` `frac-2neg` `associate-/r*` `flip--` `div-inv`
1×	`sub-neg` `remove-double-div` `inv-pow`

Counts

3 → 20

Calls

3 calls:

4.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
4.0ms	(/ (sin x) (- 1.0 (cos x)))
2.0ms	(- 1.0 (cos x))

series89.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
34.0ms	(/ (sin x) (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify63.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	145	122
1	470	119
2	1902	117
3	5001	117

prune63.0ms

Filtered

29 candidates to 18 candidates (62.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	27	10	37

Merged error: 0.2b

Counts

37 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- 1.0 (cos x)))
0.1b	(/ 1 (sin x))
0.2b	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
2.2b	(- 1.0 (cos x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-/r/` `div-inv`
5×	`frac-2neg` `clear-num`
4×	`flip3--` `flip--`
3×	`times-frac` `associate-/r*` `associate-/l/`
2×	`inv-pow`
1×	`sub-neg` `associate-/l*`

Counts

4 → 30

Calls

4 calls:

3.0ms	(/ 1 (- 1.0 (cos x)))
2.0ms	(/ 1 (sin x))
5.0ms	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
2.0ms	(- 1.0 (cos x))

series96.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (- 1.0 (cos x)))
13.0ms	(/ 1 (sin x))
38.0ms	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
18.0ms	(- 1.0 (cos x))

simplify134.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	198	182
1	776	168
2	4013	167
3	5002	167

prune63.0ms

Filtered

42 candidates to 24 candidates (57.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	40	12	52

Merged error: 0.2b

Counts

52 → 12

regimes110.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.7b

bsearch59.0ms

Steps

Iters	Range		Point
9	2.5653698016906928e-06	357.20278190505735	0.0230298891429469
7	-0.6319501064166059	-0.005814372128176944	-0.02054167097202016

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	9
1	26	9

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.0s	1564×	body	2560	valid
1.3s	2838×	body	1280	valid
423.0ms	1870×	body	640	valid
146.0ms	931×	body	320	valid
50.0ms	464×	body	160	valid
21.0ms	332×	body	80	valid
3.0ms	1×	body	5120	valid