Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
4.0ms	273×	body	80	nan

simplify4.0ms

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)))

series30.0ms

Counts

1 → 3

Calls

1 calls:

29.0ms

(/ a (- (acos a)))

simplify113.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (43.0ms)

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

prune124.0ms

Filtered

60 candidates to 44 candidates (73.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	52	8	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	9	61

Merged error: 0.0b

Counts

61 → 9

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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:

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

series65.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- (acos a)) a)
25.0ms	(/ 1 (/ (- (acos a)) a))

simplify82.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (64.0ms)

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

prune309.0ms

Filtered

245 candidates to 112 candidates (45.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	239	6	245
Fresh	5	2	7
Picked	0	1	1
Done	0	1	1
Total	244	10	254

Merged error: 0.0b

Counts

254 → 10

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`
556×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
141×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
51×	`div-inv`
47×	`neg-mul-1`
46×	`add-exp-log`
43×	`associate-/l*`
36×	`associate-/r*`
34×	`div-exp`
16×	`add-cbrt-cube` `associate-/l/`
9×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r/`
4×	`frac-2neg` `clear-num`
3×	`pow1`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

2 → 607

Calls

2 calls:

5.0ms	(/ 1 (- (acos a)))
23.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))

series31.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(/ 1 (- (acos a)))
25.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))

simplify128.0ms

Algorithm

egg-herbie

Counts

613 → 613

Iterations

Useful iterations: 1 (60.0ms)

Iter	Nodes	Cost
0	2569	7515
1	5001	6358

prune713.0ms

Filtered

613 candidates to 238 candidates (38.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	609	4	613
Fresh	5	2	7
Picked	1	0	1
Done	0	2	2
Total	615	8	623

Merged error: 0b

Counts

623 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
60×	`add-sqr-sqrt`
58×	`add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
22×	`associate-/r*`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`associate-/l*`
4×	`expm1-log1p-u` `neg-mul-1` `pow-flip` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `frac-2neg` `1-exp` `clear-num` `div-inv` `inv-pow`

Counts

4 → 162

Calls

4 calls:

2.0ms	(sqrt (acos a))
2.0ms	(sqrt (acos a))
5.0ms	(/ 1 (sqrt (acos a)))
7.0ms	(/ 1 (- (sqrt (acos a))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (acos a))
11.0ms	(sqrt (acos a))
16.0ms	(/ 1 (sqrt (acos a)))
38.0ms	(/ 1 (- (sqrt (acos a))))

simplify83.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	229	1096
1	764	999
2	1586	866
3	2862	866
4	5001	866

prune246.0ms

Filtered

174 candidates to 76 candidates (43.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	175	7	182

Merged error: 0b

Counts

182 → 7

regimes55.0ms

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

sample461.0ms

Algorithm

intervals

Results

169.0ms	8000×	body	80	valid
116.0ms	7716×	body	80	nan