Details

sample51.0ms

Algorithm

intervals

Results

23.0ms	52×	body	2560	valid
10.0ms	47×	body	1280	valid
6.0ms	45×	body	640	valid
2.0ms	24×	body	320	valid
2.0ms	70×	body	80	valid
1.0ms	18×	body	160	valid

simplify7.0ms

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: 32.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b	(- 1.0 (cos x))
16.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite6.0ms

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))

series67.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
49.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify160.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	124	81
1	396	81
2	1050	81
3	4200	80
4	5001	80

prune48.0ms

Filtered

18 candidates to 13 candidates (72.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	12	6	18
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	6	19

Merged error: 0.0b

Counts

19 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
12.6b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-r`
2×	`associate--l+` `*-commutative` `sqr-pow`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `unpow2`

Counts

3 → 11

Calls

3 calls:

3.0ms	(* 1/720 (pow x 4))
3.0ms	(* 1/24 (pow x 2))
5.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series109.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 1/720 (pow x 4))
25.0ms	(* 1/24 (pow x 2))
48.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify77.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	94	92
1	353	90
2	1717	86
3	5001	86

prune41.0ms

Filtered

20 candidates to 10 candidates (50.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	20	6	26

Merged error: 0.0b

Counts

26 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
12.6b	(- (* 1/720 (pow x 4)) (* 1/24 (pow x 2)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-r`
2×	`*-commutative` `sqr-pow`
1×	`sub-neg` `flip3--` `flip--` `unpow2`

Counts

3 → 9

Calls

3 calls:

3.0ms	(* 1/720 (pow x 4))
3.0ms	(* 1/24 (pow x 2))
5.0ms	(- (* 1/720 (pow x 4)) (* 1/24 (pow x 2)))

series179.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 1/720 (pow x 4))
25.0ms	(* 1/24 (pow x 2))
117.0ms	(- (* 1/720 (pow x 4)) (* 1/24 (pow x 2)))

simplify68.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	87	72
1	292	67
2	1404	64
3	5001	62

prune35.0ms

Filtered

18 candidates to 8 candidates (44.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

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

Merged error: 0.0b

Counts

24 → 6

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)
2.2b	(- 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))

simplify64.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	163	118
1	458	117
2	1640	115
3	5001	114

prune43.0ms

Filtered

29 candidates to 20 candidates (69.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	28	7	35

Merged error: 0.0b

Counts

35 → 7

regimes37.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.6b

bsearch58.0ms

Steps

Iters	Range		Point
9	2.5653698016906928e-06	357.20278190505735	0.03297101109879089
7	-0.6319501064166059	-0.005814372128176944	-0.03299151901246776

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	16
1	35	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

714.0ms	1565×	body	2560	valid
306.0ms	1299×	body	1280	valid
216.0ms	1465×	body	640	valid
99.0ms	931×	body	320	valid
69.0ms	2271×	body	80	valid
34.0ms	469×	body	160	valid