Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
4.0ms	288×	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: 0.2b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b	(/ a (- (acos a)))

rewrite6.0ms

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:

5.0ms

(/ a (- (acos a)))

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(/ a (- (acos a)))

simplify92.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (32.0ms)

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

prune86.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	53	5	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	6	59

Merged error: 0.0b

Counts

59 → 6

localize6.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (/ (- (acos a)) a))
0.3b	(/ (- (acos a)) a)

rewrite29.0ms

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:

10.0ms	(/ 1 (/ (- (acos a)) a))
5.0ms	(/ (- (acos a)) a)

series57.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(/ 1 (/ (- (acos a)) a))
34.0ms	(/ (- (acos a)) a)

simplify74.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	659	1916
1	3060	1699
2	5002	1507

prune217.0ms

Filtered

223 candidates to 107 candidates (48.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	218	5	223
Fresh	0	4	4
Picked	0	1	1
Done	1	0	1
Total	219	10	229

Merged error: 0b

Counts

229 → 10

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (- (acos a)))
0.4b	(/ (/ 1 (- (acos a))) (/ 1 a))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

1207×	`times-frac`
550×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
138×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
51×	`div-inv`
46×	`add-exp-log` `neg-mul-1`
37×	`associate-/l*`
34×	`div-exp`
23×	`associate-/r*`
16×	`add-cbrt-cube`
9×	`cbrt-undiv` `rec-exp` `1-exp`
3×	`pow1`
2×	`frac-2neg` `clear-num` `add-log-exp`
1×	`pow-flip` `associate-/r/` `associate-/l/` `inv-pow`

Counts

2 → 580

Calls

2 calls:

5.0ms	(/ 1 (- (acos a)))
21.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))

series28.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ 1 (- (acos a)))
23.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))

simplify116.0ms

Algorithm

egg-herbie

Counts

586 → 586

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2517	7392
1	5002	6273

prune504.0ms

Filtered

586 candidates to 225 candidates (38.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	585	1	586
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	588	8	596

Merged error: 0b

Counts

596 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- (acos a)))
0.4b	(/ (cbrt (pow (/ 1 (- (acos a))) 3)) (/ 1 a))
1.0b	(cbrt (pow (/ 1 (- (acos a))) 3))
1.0b	(pow (/ 1 (- (acos a))) 3)

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

2693×	`times-frac`
1243×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1110×	`cbrt-prod`
544×	`unpow-prod-down` `cube-prod`
300×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
112×	`div-inv`
100×	`neg-mul-1`
80×	`associate-/l*`
23×	`associate-/r*`
22×	`add-exp-log`
16×	`cube-mult` `unpow3` `sqr-pow`
12×	`add-cbrt-cube`
10×	`div-exp`
7×	`pow1`
5×	`cbrt-undiv`
4×	`pow-exp` `add-log-exp`
3×	`cube-div` `rec-exp` `pow-unpow` `pow-pow` `1-exp`
2×	`cbrt-div` `pow-flip` `frac-2neg` `clear-num` `inv-pow` `rem-cube-cbrt`
1×	`pow-to-exp` `pow1/3` `associate-/r/` `rem-cbrt-cube` `associate-/l/`

Counts

4 → 1344

Calls

4 calls:

5.0ms	(/ 1 (- (acos a)))
47.0ms	(/ (cbrt (pow (/ 1 (- (acos a))) 3)) (/ 1 a))
10.0ms	(cbrt (pow (/ 1 (- (acos a))) 3))
9.0ms	(pow (/ 1 (- (acos a))) 3)

series330.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1 (- (acos a)))
60.0ms	(/ (cbrt (pow (/ 1 (- (acos a))) 3)) (/ 1 a))
231.0ms	(cbrt (pow (/ 1 (- (acos a))) 3))
34.0ms	(pow (/ 1 (- (acos a))) 3)

simplify206.0ms

Algorithm

egg-herbie

Counts

1356 → 1356

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2458	15178
1	5001	12559

prune437.0ms

Filtered

1356 candidates to 178 candidates (13.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	1356	0	1356
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	1356	8	1364

Merged error: 0b

Counts

1364 → 8

regimes73.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	4
1	10	4

end0.0ms

sample455.0ms

Algorithm

intervals

Results

159.0ms	8000×	body	80	valid
121.0ms	7915×	body	80	nan