Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
4.0ms	244×	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 (100.0%)

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)))

series26.0ms

Counts

1 → 3

Calls

1 calls:

26.0ms

(/ a (- (acos a)))

simplify105.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	166	384
1	493	372
2	1439	367
3	3705	366
4	5002	366

prune92.0ms

Filtered

60 candidates to 44 candidates (26.7%)

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

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

252×	`times-frac`
146×	`*-un-lft-identity`
144×	`add-sqr-sqrt` `add-cube-cbrt`
52×	`distribute-rgt-neg-in`
51×	`distribute-lft-neg-in`
40×	`associate-/r*`
25×	`associate-/l*`
17×	`neg-mul-1`
16×	`associate-/r/`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv`
4×	`cbrt-undiv` `clear-num`
3×	`pow1` `frac-2neg` `remove-double-div`
2×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
1×	`neg-sub0` `pow-flip` `div-sub` `distribute-frac-neg` `inv-pow`

Counts

2 → 239

Calls

2 calls:

12.0ms	(/ 1 (/ (- (acos a)) a))
5.0ms	(/ (- (acos a)) a)

series68.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ 1 (/ (- (acos a)) a))
42.0ms	(/ (- (acos a)) a)

simplify87.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	670	1985
1	3079	1764
2	5001	1572

prune223.0ms

Filtered

245 candidates to 113 candidates (53.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	237	8	245
Fresh	7	1	8
Picked	1	0	1
Done	0	1	1
Total	245	10	255

Merged error: 0.0b

Counts

255 → 10

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

2108×	`times-frac`
1424×	`add-sqr-sqrt`
1214×	`*-un-lft-identity`
1004×	`add-cube-cbrt`
840×	`cbrt-prod`
315×	`unswap-sqr`
312×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
210×	`swap-sqr` `associate-r` `associate-l`
104×	`neg-mul-1`
52×	`associate-/l*`
40×	`associate-/r*`
35×	`*-commutative` `div-inv`
29×	`add-cbrt-cube`
16×	`cbrt-undiv` `add-exp-log` `associate-/r/`
8×	`cbrt-unprod`
7×	`div-exp`
3×	`frac-2neg` `clear-num`
2×	`pow1` `expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
1×	`neg-sub0` `div-sub` `distribute-frac-neg`

Counts

2 → 1255

Calls

2 calls:

47.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (- (acos a)) a))
5.0ms	(/ (- (acos a)) a)

series72.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (- (acos a)) a))
44.0ms	(/ (- (acos a)) a)

simplify258.0ms

Algorithm

egg-herbie

Counts

1261 → 1261

Iterations

Useful iterations: 1 (81.0ms)

Iter	Nodes	Cost
0	3831	19684
1	5002	18658

prune1.5s

Filtered

1261 candidates to 557 candidates (55.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	1254	7	1261
Fresh	6	2	8
Picked	0	1	1
Done	0	1	1
Total	1260	11	1271

Merged error: 0.0b

Counts

1271 → 11

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

20243×	`times-frac`
8461×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5691×	`cbrt-prod`
1701×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
572×	`associate-/l*`
567×	`neg-mul-1`
516×	`div-inv`
294×	`associate-/r/`
234×	`associate-/r*`
73×	`associate-/l/`
58×	`add-cbrt-cube`
51×	`cbrt-undiv`
46×	`add-exp-log`
33×	`div-exp`
19×	`frac-2neg` `clear-num`
3×	`rec-exp` `1-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`

Counts

2 → 6324

Calls

2 calls:

23.0ms	(/ (cbrt 1) (/ (- (acos a)) (cbrt 1)))
206.0ms	(/ (/ (cbrt 1) (/ (- (acos a)) (cbrt 1))) (/ 1 a))

series42.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(/ (cbrt 1) (/ (- (acos a)) (cbrt 1)))
27.0ms	(/ (/ (cbrt 1) (/ (- (acos a)) (cbrt 1))) (/ 1 a))

simplify1.3s

Algorithm

egg-herbie

Counts

6330 → 6330

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	6877	135807

prune18.6s

Filtered

6330 candidates to 4913 candidates (22.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	6327	3	6330
Fresh	5	3	8
Picked	1	0	1
Done	0	2	2
Total	6333	8	6341

Merged error: 0b

Counts

6341 → 8

regimes69.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	4	3

end0.0ms

sample499.0ms

Algorithm

intervals

Results

182.0ms	8000×	body	80	valid
128.0ms	7941×	body	80	nan