Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	273×	body	80	nan
5.0ms	256×	body	80	valid

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)))

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)))

simplify89.0ms

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

prune109.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	50	8	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	9	59

Merged error: 0.0b

Counts

59 → 9

localize5.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- (acos a)) a)
0.5b	(/ 1 (/ (- (acos a)) a))

rewrite25.0ms

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:

4.0ms	(/ (- (acos a)) a)
9.0ms	(/ 1 (/ (- (acos a)) a))

series61.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ (- (acos a)) a)
28.0ms	(/ 1 (/ (- (acos a)) a))

simplify64.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	659	1916
1	3060	1699
2	5001	1507

prune259.0ms

Filtered

223 candidates to 106 candidates (47.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	218	5	223
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	222	10	232

Merged error: 0.0b

Counts

232 → 10

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite71.0ms

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

Counts

2 → 580

Calls

2 calls:

4.0ms	(/ 1 (- (acos a)))
18.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))

series30.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ 1 (- (acos a)))
24.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))

simplify108.0ms

Algorithm

egg-herbie

Counts

586 → 586

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	2517	7392
1	5002	6273

prune620.0ms

Filtered

586 candidates to 225 candidates (38.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	583	3	586
Fresh	5	2	7
Picked	1	0	1
Done	0	2	2
Total	589	7	596

Merged error: 0b

Counts

596 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (acos a))
1.0b	(sqrt (acos a))
1.0b	(/ (* (cbrt 1) (cbrt 1)) (sqrt (acos a)))
1.0b	(/ (cbrt 1) (- (sqrt (acos a))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
81×	`add-sqr-sqrt`
79×	`add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
51×	`cbrt-prod`
42×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
22×	`associate-/r*`
11×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`neg-mul-1` `associate-/l*`
6×	`pow1`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`prod-exp` `cbrt-unprod`

Counts

4 → 183

Calls

4 calls:

1.0ms	(sqrt (acos a))
1.0ms	(sqrt (acos a))
7.0ms	(/ (* (cbrt 1) (cbrt 1)) (sqrt (acos a)))
7.0ms	(/ (cbrt 1) (- (sqrt (acos a))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (acos a))
10.0ms	(sqrt (acos a))
16.0ms	(/ (* (cbrt 1) (cbrt 1)) (sqrt (acos a)))
34.0ms	(/ (cbrt 1) (- (sqrt (acos a))))

simplify54.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	326	1767
1	1093	1653
2	3943	1173
3	5001	1166

prune232.0ms

Filtered

195 candidates to 72 candidates (36.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	196	6	202

Merged error: 0b

Counts

202 → 6

regimes49.0ms

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

sample449.0ms

Algorithm

intervals

Results

163.0ms	8000×	body	80	valid
114.0ms	7716×	body	80	nan