Details

sample138.0ms

Algorithm

intervals

Results

77.0ms	64×	body	2560	valid
37.0ms	91×	body	1280	valid
11.0ms	50×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	10×	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: 32.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite11.0ms

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:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
2.0ms	(- 1.0 (cos x))

series53.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 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

prune55.0ms

Filtered

16 candidates to 11 candidates (68.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

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

Merged error: 0.3b

Counts

17 → 8

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.2b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`fma-udef`

Counts

2 → 2

Calls

2 calls:

1.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
1.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

series176.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
123.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

simplify186.0ms

Algorithm

egg-herbie

Counts

8 → 8

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	28
1	77	28
2	169	28
3	384	28
4	1448	28
5	4794	28
6	5001	28

prune24.0ms

Filtered

8 candidates to 3 candidates (37.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

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

Merged error: 0.3b

Counts

16 → 8

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.1b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
1.5b	(- 1.0 (cos x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 23

Calls

3 calls:

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

series69.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ 1 (sin x))
38.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
18.0ms	(- 1.0 (cos x))

simplify83.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	159	150
1	603	146
2	3062	146
3	5002	145

prune65.0ms

Filtered

32 candidates to 18 candidates (56.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	31	9	40

Merged error: 0.3b

Counts

40 → 9

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin x) (- 1.0 (cos x)))
0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
1.5b	(- 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	(/ (sin x) (- 1.0 (cos x)))
4.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
2.0ms	(- 1.0 (cos x))

series90.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ (sin x) (- 1.0 (cos x)))
38.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
18.0ms	(- 1.0 (cos x))

simplify62.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 2 (15.0ms)

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

prune51.0ms

Filtered

29 candidates to 19 candidates (65.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	29	9	38

Merged error: 0.3b

Counts

38 → 9

regimes92.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 31.3b

bsearch60.0ms

Steps

Iters	Range		Point
6	0.018000635171863108	0.09117784756913819	0.02109815153064932
10	-1421.6155834850151	-1.485944467815708e-07	-0.020610258751472033

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	17
1	31	17

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1640×	body	2560	valid
1.2s	2761×	body	1280	valid
415.0ms	1824×	body	640	valid
141.0ms	913×	body	320	valid
52.0ms	483×	body	160	valid
24.0ms	376×	body	80	valid
10.0ms	3×	body	5120	valid