Details

sample18.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
4.0ms	244×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize4.0ms

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` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 57

Calls

1 calls:

5.0ms

(/ a (- (acos a)))

series28.0ms

Counts

1 → 3

Calls

1 calls:

28.0ms

(/ a (- (acos a)))

simplify112.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	166	384
1	493	372
2	1439	367
3	3705	366
4	5002	366

prune93.0ms

Filtered

60 candidates to 44 candidates (73.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	53	7	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	8	61

Merged error: 0.0b

Counts

61 → 8

localize6.0ms

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`
146×	`*-un-lft-identity`
144×	`add-sqr-sqrt` `add-cube-cbrt`
52×	`distribute-rgt-neg-in`
51×	`distribute-lft-neg-in`
40×	`associate-/r*`
25×	`associate-/l*`
17×	`neg-mul-1`
16×	`associate-/r/`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv`
4×	`cbrt-undiv` `clear-num`
3×	`pow1` `frac-2neg` `remove-double-div`
2×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
1×	`neg-sub0` `pow-flip` `div-sub` `distribute-frac-neg` `inv-pow`

Counts

2 → 239

Calls

2 calls:

5.0ms	(/ (- (acos a)) a)
13.0ms	(/ 1 (/ (- (acos a)) a))

series71.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- (acos a)) a)
33.0ms	(/ 1 (/ (- (acos a)) a))

simplify91.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	670	1985
1	3079	1764
2	5001	1572

prune225.0ms

Filtered

245 candidates to 114 candidates (46.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	238	7	245
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	242	11	253

Merged error: 0.0b

Counts

253 → 11

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

148×	`times-frac`
127×	`add-sqr-sqrt`
99×	`*-un-lft-identity`
92×	`add-cube-cbrt`
65×	`associate-r`
50×	`associate-l`
46×	`add-exp-log`
37×	`associate-/r*`
18×	`associate-*r/` `div-exp`
16×	`prod-exp` `add-cbrt-cube`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `unswap-sqr`
12×	`associate-/r/`
11×	`associate-/l*`
9×	`rec-exp` `1-exp`
7×	`pow1`
6×	`un-div-inv` `div-inv`
5×	`cbrt-undiv` `neg-mul-1` `clear-num` `*-commutative`
4×	`cbrt-unprod`
3×	`frac-2neg`
2×	`expm1-log1p-u` `pow-flip` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
1×	`distribute-lft-neg-out` `inv-pow`

Counts

2 → 228

Calls

2 calls:

19.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
11.0ms	(* (- (acos a)) (/ 1 a))

series72.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
45.0ms	(* (- (acos a)) (/ 1 a))

simplify87.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	723	1813
1	3279	1446
2	5001	1207

prune203.0ms

Filtered

234 candidates to 100 candidates (42.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	229	5	234
Fresh	4	4	8
Picked	0	1	1
Done	1	1	2
Total	234	11	245

Merged error: 0.0b

Counts

245 → 11

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

1231×	`times-frac`
699×	`add-sqr-sqrt`
562×	`*-un-lft-identity`
538×	`add-cube-cbrt`
299×	`associate-r`
228×	`sqrt-prod`
69×	`associate-l` `unswap-sqr`
49×	`div-inv`
36×	`add-exp-log`
34×	`associate-/l*`
28×	`associate-/r*`
23×	`*-commutative`
22×	`add-cbrt-cube`
19×	`div-exp`
12×	`associate-/r/` `associate-/l/`
11×	`cbrt-undiv`
9×	`associate-*r/`
8×	`prod-exp`
4×	`clear-num` `cbrt-unprod`
3×	`frac-2neg` `un-div-inv`
2×	`rec-exp` `1-exp`
1×	`pow1` `expm1-log1p-u` `mul-1-neg` `distribute-frac-neg` `log1p-expm1-u` `add-log-exp`

Counts

1 → 627

Calls

1 calls:

35.0ms

(/ (* -1 (/ 1 (acos a))) (/ (sqrt 1) a))

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(/ (* -1 (/ 1 (acos a))) (/ (sqrt 1) a))

simplify155.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 1 (68.0ms)

Iter	Nodes	Cost
0	2974	9078
1	5002	7470

prune639.0ms

Filtered

630 candidates to 237 candidates (37.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	628	2	630
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	629	12	641

Merged error: 0.0b

Counts

641 → 12

regimes90.0ms

Accuracy

0% (0.2b 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	4	3

end0.0ms

sample451.0ms

Algorithm

intervals

Results

166.0ms	8000×	body	80	valid
114.0ms	7849×	body	80	nan