Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
4.0ms	249×	body	80	nan

simplify2.0ms

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

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

1×	`neg-mul-1` `frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

1 → 4

Calls

1 calls:

2.0ms

(/ a (- (acos a)))

series25.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

(/ a (- (acos a)))

simplify9.0ms

Algorithm

egg-herbie

Counts

7 → 7

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	18
1	29	18
2	38	18
3	43	18
4	44	18
5	44	18

prune12.0ms

Filtered

7 candidates to 5 candidates (71.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	6	1	7
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	6	2	8

Merged error: 0.2b

Counts

8 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`clear-num` `associate-/r/`
3×	`frac-2neg` `div-inv`
2×	`neg-mul-1` `associate-/l*`
1×	`neg-sub0` `div-sub` `distribute-frac-neg` `associate-/r*` `remove-double-div` `inv-pow`

Counts

2 → 16

Calls

2 calls:

6.0ms	(/ 1 (/ (- (acos a)) a))
2.0ms	(/ (- (acos a)) a)

series55.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(/ 1 (/ (- (acos a)) a))
32.0ms	(/ (- (acos a)) a)

simplify163.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	37	50
1	121	48
2	409	44
3	653	44
4	2365	44
5	5001	44

prune33.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	20	4	24

Merged error: 0.1b

Counts

24 → 4

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`div-inv`
4×	`frac-2neg` `clear-num`
3×	`associate-/r/` `associate-/l/`
1×	`times-frac` `associate-/r` `associate-/l`

Counts

2 → 15

Calls

2 calls:

2.0ms	(/ -1 (acos a))
4.0ms	(/ (/ -1 (acos a)) (/ 1 a))

series28.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(/ -1 (acos a))
23.0ms	(/ (/ -1 (acos a)) (/ 1 a))

simplify86.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	60	60
1	209	51
2	497	47
3	733	47
4	1036	47
5	1887	47
6	5001	47

prune22.0ms

Filtered

21 candidates to 10 candidates (47.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	21	4	25

Merged error: 0.1b

Counts

25 → 4

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-*r/`
5×	`clear-num` `associate-/r/`
4×	`associate-/r*` `un-div-inv`
3×	`frac-2neg` `div-inv`
2×	`neg-mul-1` `associate-r` `associate-l` `*-commutative`
1×	`distribute-lft-neg-out` `inv-pow`

Counts

2 → 22

Calls

2 calls:

4.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
3.0ms	(* (- (acos a)) (/ 1 a))

series58.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
32.0ms	(* (- (acos a)) (/ 1 a))

simplify90.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (16.0ms)

Iter	Nodes	Cost
0	55	70
1	205	61
2	721	52
3	1490	51
4	1787	51
5	2638	51
6	5001	51

prune24.0ms

Filtered

28 candidates to 13 candidates (46.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	28	4	32

Merged error: 0.1b

Counts

32 → 4

regimes31.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.1b 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

sample449.0ms

Algorithm

intervals

Results

156.0ms	8000×	body	80	valid
115.0ms	8139×	body	80	nan