Details

sample22.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
6.0ms	261×	body	80	nan

simplify3.0ms

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: 0.2b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b	(/ 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)))

series31.0ms

Counts

1 → 3

Calls

1 calls:

31.0ms

(/ a (- (acos a)))

simplify103.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	166	384
1	493	372
2	1442	367
3	3704	366
4	5002	366

prune116.0ms

Filtered

60 candidates to 44 candidates (73.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	51	9	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	10	61

Merged error: 0.0b

Counts

61 → 10

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite31.0ms

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×	`expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`neg-sub0` `pow-flip` `div-sub` `distribute-frac-neg` `associate-/r/` `inv-pow`

Counts

2 → 221

Calls

2 calls:

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

series64.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (- (acos a)) a)
27.0ms	(/ 1 (/ (- (acos a)) a))

simplify85.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	663	1934
1	3064	1717
2	5001	1525

prune269.0ms

Filtered

227 candidates to 110 candidates (48.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	221	6	227
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	225	12	237

Merged error: 0.0b

Counts

237 → 12

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite76.0ms

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×	`expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `associate-/r/` `associate-/l/` `inv-pow`

Counts

2 → 584

Calls

2 calls:

5.0ms	(/ 1 (- (acos a)))
20.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))

series32.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(/ 1 (- (acos a)))
26.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))

simplify129.0ms

Algorithm

egg-herbie

Counts

590 → 590

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	2521	7412
1	5002	6293

prune605.0ms

Filtered

590 candidates to 229 candidates (38.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	588	2	590
Fresh	6	3	9
Picked	0	1	1
Done	0	2	2
Total	594	8	602

Merged error: 0.0b

Counts

602 → 8

localize9.0ms

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

rewrite217.0ms

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×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `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 → 1352

Calls

4 calls:

6.0ms	(/ 1 (- (acos a)))
45.0ms	(/ (cbrt (pow (/ 1 (- (acos a))) 3)) (/ 1 a))
9.0ms	(pow (/ 1 (- (acos a))) 3)
10.0ms	(cbrt (pow (/ 1 (- (acos a))) 3))

series161.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1 (- (acos a)))
69.0ms	(/ (cbrt (pow (/ 1 (- (acos a))) 3)) (/ 1 a))
38.0ms	(pow (/ 1 (- (acos a))) 3)
48.0ms	(cbrt (pow (/ 1 (- (acos a))) 3))

simplify234.0ms

Algorithm

egg-herbie

Counts

1364 → 1364

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	2466	15220
1	5002	12601

prune552.0ms

Filtered

1364 candidates to 186 candidates (13.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1361	3	1364
Fresh	4	0	4
Picked	0	1	1
Done	1	2	3
Total	1366	6	1372

Merged error: 0b

Counts

1372 → 6

regimes52.0ms

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

sample564.0ms

Algorithm

intervals

Results

215.0ms	8000×	body	80	valid
163.0ms	8277×	body	80	nan