Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
6.0ms	312×	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)))

rewrite10.0ms

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:

8.0ms

(/ a (- (acos a)))

series27.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(/ a (- (acos a)))

simplify108.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (40.0ms)

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

prune109.0ms

Filtered

60 candidates to 44 candidates (73.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	54	6	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	7	61

Merged error: 0.0b

Counts

61 → 7

localize6.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ 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×	`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:

10.0ms	(/ 1 (/ (- (acos a)) a))
8.0ms	(/ (- (acos a)) a)

series65.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ 1 (/ (- (acos a)) a))
35.0ms	(/ (- (acos a)) a)

simplify79.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 2 (60.0ms)

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

prune255.0ms

Filtered

227 candidates to 111 candidates (48.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	223	4	227
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	224	10	234

Merged error: 0.0b

Counts

234 → 10

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

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×	`expm1-log1p-u` `pow-flip` `associate-*r/` `pow-prod-down` `associate-/r/` `un-div-inv` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`distribute-lft-neg-out` `neg-mul-1` `frac-2neg` `clear-num` `associate-/r` `-commutative` `inv-pow`

Counts

2 → 88

Calls

2 calls:

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

series64.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
39.0ms	(* (- (acos a)) (/ 1 a))

simplify46.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	355	529
1	1644	425
2	5001	401

prune116.0ms

Filtered

94 candidates to 48 candidates (51.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	94	10	104

Merged error: 0.0b

Counts

104 → 10

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ a (- (acos a)))) (cbrt (/ a (- (acos a)))))
0.7b	(cbrt (/ a (- (acos a))))
0.7b	(cbrt (/ a (- (acos a))))
0.7b	(cbrt (/ a (- (acos a))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

262×	`cbrt-prod`
228×	`times-frac`
176×	`add-sqr-sqrt`
164×	`*-un-lft-identity`
152×	`add-cube-cbrt`
69×	`distribute-rgt-neg-in`
63×	`distribute-lft-neg-in`
43×	`swap-sqr`
37×	`associate-r` `associate-l`
21×	`neg-mul-1`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 284

Calls

4 calls:

31.0ms	(* (cbrt (/ a (- (acos a)))) (cbrt (/ a (- (acos a)))))
4.0ms	(cbrt (/ a (- (acos a))))
4.0ms	(cbrt (/ a (- (acos a))))
5.0ms	(cbrt (/ a (- (acos a))))

series769.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(* (cbrt (/ a (- (acos a)))) (cbrt (/ a (- (acos a)))))
177.0ms	(cbrt (/ a (- (acos a))))
170.0ms	(cbrt (/ a (- (acos a))))
176.0ms	(cbrt (/ a (- (acos a))))

simplify83.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	471	3435
1	1666	3365
2	5002	3226

prune714.0ms

Filtered

296 candidates to 223 candidates (75.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	295	1	296
Fresh	1	5	6
Picked	0	1	1
Done	1	2	3
Total	297	9	306

Merged error: 0b

Counts

306 → 9

regimes64.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b 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

sample528.0ms

Algorithm

intervals

Results

204.0ms	8000×	body	80	valid
150.0ms	8149×	body	80	nan