Details

sample57.0ms

Algorithm

intervals

Results

26.0ms	48×	body	2560	valid
9.0ms	37×	body	1280	valid
8.0ms	51×	body	640	valid
3.0ms	29×	body	320	valid
3.0ms	75×	body	80	valid
1.0ms	16×	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: 29.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1.0 (cos x))
14.5b	(/ (- 1.0 (cos x)) (* x x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

4.0ms	(- 1.0 (cos x))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317

prune120.0ms

Filtered

64 candidates to 43 candidates (67.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	53	11	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	11	65

Merged error: 0.1b

Counts

65 → 11

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)
1.2b	(- 1.0 (cos x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
110×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-neg` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 165

Calls

3 calls:

8.0ms	(/ (/ (- 1.0 (cos x)) x) x)
6.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series106.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (/ (- 1.0 (cos x)) x) x)
40.0ms	(/ (- 1.0 (cos x)) x)
21.0ms	(- 1.0 (cos x))

simplify61.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	592	1453
1	2212	1292
2	5001	1283

prune256.0ms

Filtered

174 candidates to 115 candidates (66.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	169	5	174
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	173	12	185

Merged error: 0.1b

Counts

185 → 12

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b	(/ (cos x) x)
1.4b	(- (/ 1.0 x) (/ (cos x) x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

338×	`times-frac`
287×	`add-sqr-sqrt`
267×	`*-un-lft-identity`
227×	`add-cube-cbrt`
169×	`prod-diff`
39×	`div-inv`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/l*`
13×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`distribute-rgt-out--` `add-log-exp`
4×	`associate-/l/`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub`

Counts

3 → 306

Calls

3 calls:

28.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
4.0ms	(/ (cos x) x)
16.0ms	(- (/ 1.0 x) (/ (cos x) x))

series183.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
28.0ms	(/ (cos x) x)
60.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify128.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	1009	6352
1	3221	4216
2	5001	3627

prune339.0ms

Filtered

315 candidates to 138 candidates (43.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	311	4	315
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	314	13	327

Merged error: 0.1b

Counts

327 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
1.2b	(- 1.0 (cos x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`cbrt-prod` `prod-diff`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
4.0ms	(- 1.0 (cos x))

series536.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt x)
175.0ms	(cbrt x)
173.0ms	(cbrt x)
18.0ms	(- 1.0 (cos x))

simplify87.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	183	370
1	534	270
2	2582	252
3	5001	237

prune139.0ms

Filtered

79 candidates to 60 candidates (75.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	78	14	92

Merged error: 0.1b

Counts

92 → 14

regimes61.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 30.5b

bsearch77.0ms

Steps

Iters	Range		Point
11	3.029362037509861e-19	14.716166499582775	0.03237818898930031
11	-2193661101726697.2	-1.4639597033977343e-08	-0.03230798590936423

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	9
1	26	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

775.0ms	1605×	body	2560	valid
307.0ms	1192×	body	1280	valid
252.0ms	1500×	body	640	valid
106.0ms	924×	body	320	valid
87.0ms	2315×	body	80	valid
38.0ms	464×	body	160	valid