Details

sample22.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
6.0ms	312×	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: 0.2b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b	(/ 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)))

series24.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

(/ a (- (acos a)))

simplify90.0ms

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

prune93.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	52	6	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	7	59

Merged error: 0.0b

Counts

59 → 7

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

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

series63.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify68.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (50.0ms)

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

prune213.0ms

Filtered

223 candidates to 107 candidates (48.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	219	4	223
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	220	10	230

Merged error: 0.0b

Counts

230 → 10

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

series59.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
35.0ms	(* (- (acos a)) (/ 1 a))

simplify39.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (33.0ms)

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

prune90.0ms

Filtered

90 candidates to 44 candidates (48.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	90	10	100

Merged error: 0.0b

Counts

100 → 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))))

rewrite60.0ms

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×	`add-cbrt-cube` `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 → 276

Calls

4 calls:

33.0ms	(* (cbrt (/ a (- (acos a)))) (cbrt (/ a (- (acos a)))))
4.0ms	(cbrt (/ a (- (acos a))))
4.0ms	(cbrt (/ a (- (acos a))))
4.0ms	(cbrt (/ a (- (acos a))))

series719.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(* (cbrt (/ a (- (acos a)))) (cbrt (/ a (- (acos a)))))
162.0ms	(cbrt (/ a (- (acos a))))
162.0ms	(cbrt (/ a (- (acos a))))
164.0ms	(cbrt (/ a (- (acos a))))

simplify75.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	466	3386
1	1653	3317
2	5001	3176

prune632.0ms

Filtered

288 candidates to 215 candidates (74.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	287	1	288
Fresh	1	5	6
Picked	0	1	1
Done	1	2	3
Total	289	9	298

Merged error: 0b

Counts

298 → 9

regimes59.0ms

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

sample553.0ms

Algorithm

intervals

Results

212.0ms	8000×	body	80	valid
153.0ms	8149×	body	80	nan