Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
5.0ms	235×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	4	3

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: 0.3b

Counts

2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ a (- (acos a)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

30×	`times-frac`
24×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-/r*`
4×	`neg-mul-1`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`pow1` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 55

Calls

1 calls:

4.0ms

(/ a (- (acos a)))

series24.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

(/ a (- (acos a)))

simplify96.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	164	376
1	491	364
2	1440	359
3	3702	358
4	5001	358

prune92.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	50	8	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	9	59

Merged error: 0.0b

Counts

59 → 9

localize5.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (- (acos a)) a)
0.3b	(/ 1 (/ (- (acos a)) a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

252×	`times-frac`
140×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
37×	`associate-/r*`
16×	`neg-mul-1`
15×	`add-exp-log`
13×	`associate-/l*`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv`
4×	`cbrt-undiv`
3×	`pow1`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`neg-sub0` `pow-flip` `div-sub` `distribute-frac-neg` `associate-/r/` `inv-pow`

Counts

2 → 217

Calls

2 calls:

4.0ms	(/ (- (acos a)) a)
13.0ms	(/ 1 (/ (- (acos a)) a))

series62.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- (acos a)) a)
23.0ms	(/ 1 (/ (- (acos a)) a))

simplify71.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	659	1916
1	3060	1699
2	5001	1507

prune223.0ms

Filtered

223 candidates to 105 candidates (47.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	217	6	223
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	222	10	232

Merged error: 0.0b

Counts

232 → 10

localize6.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ 1 (* (- (acos a)) (/ 1 a)))
0.4b	(* (- (acos a)) (/ 1 a))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log`
21×	`add-sqr-sqrt`
18×	`div-exp`
16×	`prod-exp` `add-cbrt-cube`
15×	`*-un-lft-identity`
14×	`add-cube-cbrt` `times-frac`
13×	`associate-r`
10×	`associate-l`
9×	`rec-exp` `1-exp`
7×	`pow1`
5×	`cbrt-undiv`
4×	`cbrt-unprod`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-/l*` `unswap-sqr`
2×	`pow-flip` `associate-*r/` `pow-prod-down` `associate-/r/` `un-div-inv` `div-inv` `add-log-exp`
1×	`distribute-lft-neg-out` `neg-mul-1` `frac-2neg` `clear-num` `associate-/r` `-commutative` `inv-pow`

Counts

2 → 84

Calls

2 calls:

7.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
9.0ms	(* (- (acos a)) (/ 1 a))

series61.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
38.0ms	(* (- (acos a)) (/ 1 a))

simplify42.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	351	507
1	1640	403
2	5001	379

prune101.0ms

Filtered

90 candidates to 46 candidates (51.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	90	10	100

Merged error: 0.0b

Counts

100 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a)))
0.5b	(cbrt (/ (- (acos a)) a))
0.5b	(cbrt (/ (- (acos a)) a))
0.5b	(cbrt (/ (- (acos a)) a))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

15530×	`times-frac`
7956×	`cbrt-prod`
6359×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2106×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
702×	`neg-mul-1`
273×	`div-inv`
116×	`associate-/l*`
42×	`cbrt-div`
39×	`associate-/r/`
37×	`associate-/r*`
13×	`add-exp-log`
7×	`pow1`
6×	`div-exp` `add-cbrt-cube`
5×	`pow1/3`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-div`
2×	`pow-flip`
1×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/` `inv-pow`

Counts

4 → 4595

Calls

4 calls:

120.0ms	(/ (/ 1 (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a)))
4.0ms	(cbrt (/ (- (acos a)) a))
5.0ms	(cbrt (/ (- (acos a)) a))
4.0ms	(cbrt (/ (- (acos a)) a))

series726.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(/ (/ 1 (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a)))
166.0ms	(cbrt (/ (- (acos a)) a))
160.0ms	(cbrt (/ (- (acos a)) a))
164.0ms	(cbrt (/ (- (acos a)) a))

simplify1.0s

Algorithm

egg-herbie

Counts

4607 → 4607

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	6407	118310

prune17.1s

Filtered

4607 candidates to 3653 candidates (79.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	4604	3	4607
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	4607	10	4617

Merged error: 0b

Counts

4617 → 10

regimes71.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	3

end0.0ms

sample536.0ms

Algorithm

intervals

Results

200.0ms	8000×	body	80	valid
156.0ms	8031×	body	80	nan