Details

sample141.0ms

Algorithm

intervals

Results

72.0ms	52×	body	2560	valid
41.0ms	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))

rewrite6.0ms

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))

series62.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify144.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	118	76
1	303	76
2	834	76
3	3535	75
4	5001	75

prune50.0ms

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

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 1/240 (pow x 5))
0.1b	(* 1/24 (pow x 3))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-r`
2×	`*-commutative` `sqr-pow`
1×	`unpow3`

Counts

2 → 5

Calls

2 calls:

2.0ms	(* 1/240 (pow x 5))
3.0ms	(* 1/24 (pow x 3))

series92.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(* 1/240 (pow x 5))
38.0ms	(* 1/24 (pow x 3))

simplify133.0ms

Algorithm

egg-herbie

Counts

11 → 11

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	18
1	77	18
2	226	18
3	829	18
4	4349	18
5	5001	18

prune27.0ms

Filtered

11 candidates to 5 candidates (45.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	11	0	11
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	11	8	19

Merged error: 0.2b

Counts

19 → 8

localize8.0ms

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))

series100.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
36.0ms	(/ (sin x) (- 1.0 (cos x)))
24.0ms	(- 1.0 (cos x))

simplify62.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	137	125
1	435	123
2	1758	121
3	5001	121

prune64.0ms

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))

rewrite13.0ms

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))

series101.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1 (- 1.0 (cos x)))
19.0ms	(/ 1 (sin x))
36.0ms	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
19.0ms	(- 1.0 (cos x))

simplify133.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	189	188
1	742	176
2	3819	175
3	5001	175

prune64.0ms

Filtered

42 candidates to 24 candidates (57.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	3	4	7
Picked	0	1	1
Done	0	2	2
Total	41	11	52

Merged error: 0.2b

Counts

52 → 11

regimes107.0ms

Accuracy

99.3% (0.2b remaining)

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

bsearch67.0ms

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	32	11
1	32	11

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1564×	body	2560	valid
1.3s	2838×	body	1280	valid
441.0ms	1870×	body	640	valid
145.0ms	931×	body	320	valid
51.0ms	464×	body	160	valid
28.0ms	332×	body	80	valid
3.0ms	1×	body	5120	valid