Details

sample52.0ms

Algorithm

intervals

Results

23.0ms	52×	body	2560	valid
10.0ms	47×	body	1280	valid
7.0ms	45×	body	640	valid
3.0ms	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))

rewrite10.0ms

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))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series58.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
41.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify163.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (36.0ms)

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

prune49.0ms

Filtered

18 candidates to 13 candidates (72.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	12	6	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	7	19

Merged error: 0.0b

Counts

19 → 7

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(* 1/24 (pow x 2))
12.6b	(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))))

series68.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* 1/24 (pow x 2))
45.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify73.0ms

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

prune25.0ms

Filtered

10 candidates to 5 candidates (50.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	10	0	10
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	10	7	17

Merged error: 0.0b

Counts

17 → 7

localize7.0ms

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))

series103.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (/ (- 1.0 (cos x)) x) x)
41.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify61.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 2 (15.0ms)

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

prune55.0ms

Filtered

29 candidates to 20 candidates (69.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	24	5	29
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	27	9	36

Merged error: 0.0b

Counts

36 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
0.4b	(+ 1.0 (cos x))
0.4b	(pow (cos x) 3)
2.0b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sqr-pow`
6×	`unpow3`
4×	`prod-diff`
2×	`difference-cubes` `flip3--` `fma-neg` `flip--` `associate-/l/` `associate-/l*` `difference-of-squares`
1×	`+-commutative` `pow-to-exp` `sub-neg` `frac-2neg` `flip3-+` `div-sub` `clear-num` `flip-+` `div-inv`

Counts

4 → 26

Calls

4 calls:

6.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
2.0ms	(+ 1.0 (cos x))
2.0ms	(pow (cos x) 3)
5.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series201.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
9.0ms	(+ 1.0 (cos x))
27.0ms	(pow (cos x) 3)
49.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify132.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	236	295
1	869	265
2	4051	260
3	5001	260

prune95.0ms

Filtered

38 candidates to 28 candidates (73.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	38	9	47

Merged error: 0.0b

Counts

47 → 9

regimes66.0ms

Accuracy

99.5% (0.1b remaining)

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

bsearch54.0ms

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	32	15
1	32	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

735.0ms	1565×	body	2560	valid
296.0ms	1299×	body	1280	valid
225.0ms	1465×	body	640	valid
96.0ms	931×	body	320	valid
76.0ms	2271×	body	80	valid
34.0ms	469×	body	160	valid