Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
5.0ms	222×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	4	3

prune1.0ms

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)))

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:

4.0ms

(/ a (- (acos a)))

series22.0ms

Counts

1 → 3

Calls

1 calls:

22.0ms

(/ a (- (acos a)))

simplify89.0ms

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

prune91.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	49	9	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	10	59

Merged error: 0.0b

Counts

59 → 10

localize5.0ms

Local error

Found 2 expressions with local error:

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

9.0ms	(/ 1 (/ (- (acos a)) a))
8.0ms	(/ (- (acos a)) a)

series60.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ 1 (/ (- (acos a)) a))
32.0ms	(/ (- (acos a)) a)

simplify74.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (54.0ms)

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

prune218.0ms

Filtered

223 candidates to 106 candidates (47.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	215	8	223
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	219	14	233

Merged error: 0.0b

Counts

233 → 14

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

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))

series54.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
32.0ms	(* (- (acos a)) (/ 1 a))

simplify40.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (34.0ms)

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

prune100.0ms

Filtered

90 candidates to 44 candidates (48.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	2	9	11
Picked	0	1	1
Done	1	1	2
Total	91	13	104

Merged error: 0.0b

Counts

104 → 13

localize6.0ms

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)))
19.0ms	(/ (/ 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))

simplify124.0ms

Algorithm

egg-herbie

Counts

586 → 586

Iterations

Useful iterations: 1 (52.0ms)

Iter	Nodes	Cost
0	2517	7392
1	5002	6273

prune496.0ms

Filtered

586 candidates to 226 candidates (38.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	583	3	586
Fresh	8	2	10
Picked	0	1	1
Done	0	2	2
Total	591	8	599

Merged error: 0b

Counts

599 → 8

regimes49.0ms

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

sample557.0ms

Algorithm

intervals

Results

217.0ms	8000×	body	80	valid
159.0ms	8036×	body	80	nan