Details

sample57.0ms

Algorithm

intervals

Results

30.0ms	64×	body	2560	valid
8.0ms	39×	body	1280	valid
6.0ms	41×	body	640	valid
3.0ms	26×	body	320	valid
2.0ms	71×	body	80	valid
1.0ms	15×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	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: 33.5b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
17.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 12

Calls

2 calls:

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

series63.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify164.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	129	81
1	421	77
2	1173	77
3	4692	76
4	5001	76

prune54.0ms

Filtered

18 candidates to 13 candidates (72.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	11	7	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	8	19

Merged error: 0.2b

Counts

19 → 8

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 1/24 (pow x 2))
12.9b	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-r`
1×	`*-commutative` `fma-udef` `unpow2` `sqr-pow`

Counts

2 → 4

Calls

2 calls:

3.0ms	(* 1/24 (pow x 2))
1.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series70.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(* 1/24 (pow x 2))
46.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify72.0ms

Algorithm

egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	37	28
1	107	25
2	348	25
3	1690	25
4	5001	25

prune28.0ms

Filtered

10 candidates to 5 candidates (50.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	10	0	10
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	10	8	18

Merged error: 0.2b

Counts

18 → 8

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 20

Calls

3 calls:

4.0ms	(/ (/ (- 1.0 (cos x)) x) x)
3.0ms	(/ (- 1.0 (cos x)) x)
2.0ms	(- 1.0 (cos x))

series108.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (/ (- 1.0 (cos x)) x) x)
47.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify58.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	169	118
1	491	111
2	1801	109
3	5001	109

prune58.0ms

Filtered

29 candidates to 20 candidates (69.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	25	4	29
Fresh	4	1	5
Picked	1	0	1
Done	0	2	2
Total	30	7	37

Merged error: 0.1b

Counts

37 → 7

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 38

Calls

3 calls:

6.0ms	(/ (* (- 1.0 (cos x)) (/ 1 x)) x)
4.0ms	(* (- 1.0 (cos x)) (/ 1 x))
2.0ms	(- 1.0 (cos x))

series112.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (* (- 1.0 (cos x)) (/ 1 x)) x)
43.0ms	(* (- 1.0 (cos x)) (/ 1 x))
22.0ms	(- 1.0 (cos x))

simplify150.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	218	213
1	892	203
2	4731	201
3	5001	200

prune76.0ms

Filtered

47 candidates to 29 candidates (61.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	46	8	54

Merged error: 0.1b

Counts

54 → 8

regimes70.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.9b

bsearch56.0ms

Steps

Iters	Range		Point
6	0.018000635171863108	0.09117784756913819	0.03010910821075468
10	-1421.6155834850151	-1.485944467815708e-07	-0.03323288645356819

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	15
1	30	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

778.0ms	1643×	body	2560	valid
279.0ms	1221×	body	1280	valid
221.0ms	1450×	body	640	valid
100.0ms	914×	body	320	valid
78.0ms	2291×	body	80	valid
35.0ms	481×	body	160	valid