Details

sample55.0ms

Algorithm

intervals

Results

23.0ms	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))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 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))

simplify62.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune111.0ms

Filtered

48 candidates to 34 candidates (70.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	37	11	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	11	49

Merged error: 0.1b

Counts

49 → 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))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

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

series112.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (/ (- 1.0 (cos x)) x) x)
42.0ms	(/ (- 1.0 (cos x)) x)
23.0ms	(- 1.0 (cos x))

simplify53.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	531	1270
1	1899	1197
2	5001	1186

prune231.0ms

Filtered

156 candidates to 104 candidates (66.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	151	5	156
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	156	11	167

Merged error: 0.1b

Counts

167 → 11

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))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
95×	`times-frac`
78×	`*-un-lft-identity`
38×	`add-cube-cbrt`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/l*`
12×	`div-inv`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`distribute-rgt-out--` `add-log-exp`
4×	`associate-/l/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub`

Counts

3 → 118

Calls

3 calls:

15.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
4.0ms	(/ (cos x) x)
15.0ms	(- (/ 1.0 x) (/ (cos x) x))

series191.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
30.0ms	(/ (cos x) x)
61.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify50.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	463	1015
1	1518	940
2	5001	936

prune225.0ms

Filtered

127 candidates to 100 candidates (78.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	126	12	138

Merged error: 0.1b

Counts

138 → 12

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))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

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

series556.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
175.0ms	(cbrt x)
185.0ms	(cbrt x)
18.0ms	(- 1.0 (cos x))

simplify44.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	126	193
1	315	179
2	921	173
3	5001	173

prune118.0ms

Filtered

59 candidates to 48 candidates (81.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	58	13	71

Merged error: 0.1b

Counts

71 → 13

regimes58.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.6b

bsearch93.0ms

Steps

Iters	Range		Point
11	3.029362037509861e-19	14.716166499582775	0.03137961608040849
11	-2193661101726697.2	-1.4639597033977343e-08	-0.03230798590936423

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	25
1	42	25

end0.0ms

sample1.7s

Algorithm

intervals

Results

785.0ms	1605×	body	2560	valid
305.0ms	1192×	body	1280	valid
245.0ms	1500×	body	640	valid
108.0ms	924×	body	320	valid
93.0ms	2315×	body	80	valid
38.0ms	464×	body	160	valid