Details

sample115.0ms

Algorithm

intervals

Results

50.0ms	618×	body	80	nan
40.0ms	354×	body	80	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2753
5	970
4	328
3	124
2	62
1	31
0	13

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
0.2b	(* (* n 2) PI)
1.7b	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

493×	`times-frac`
383×	`add-sqr-sqrt`
380×	`*-un-lft-identity`
378×	`add-cube-cbrt`
328×	`unpow-prod-up`
312×	`prod-diff`
141×	`sqrt-prod`
46×	`associate-/l*`
26×	`add-exp-log`
25×	`div-inv`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sub-neg` `unpow-prod-down` `sqr-pow`
6×	`pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp`
3×	`expm1-log1p-u` `pow-pow` `associate-r` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-l` `*-commutative` `distribute-lft-out--` `associate-/l/`

Counts

3 → 436

Calls

3 calls:

25.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
14.0ms	(* (* n 2) PI)
17.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series559.0ms

Counts

3 → 9

Calls

3 calls:

320.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
38.0ms	(* (* n 2) PI)
201.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify3.8s

Counts

445 → 445

Iterations

Iter	Nodes
done	5000
2	4377
1	1539
0	699

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* n 2) PI)
0.3b	(* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
1.7b	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
1.7b	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

2180×	`times-frac`
2082×	`sqrt-prod`
1741×	`add-sqr-sqrt`
1443×	`*-un-lft-identity`
1439×	`add-cube-cbrt`
1262×	`unpow-prod-up`
1170×	`prod-diff`
393×	`swap-sqr`
286×	`associate-r`
284×	`associate-l`
94×	`div-inv`
54×	`sqr-pow`
46×	`sub-neg`
36×	`pow1` `unswap-sqr`
30×	`unpow-prod-down`
23×	`add-exp-log`
12×	`pow-unpow` `pow-prod-down`
11×	`add-cbrt-cube`
10×	`prod-exp`
8×	`sqrt-pow1` `pow1/2`
6×	`pow-pow` `pow-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sqrt-div` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-sqr`
2×	`pow-to-exp` `*-commutative` `distribute-lft-out--` `pow-sub`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `associate-r/`

Counts

4 → 1181

Calls

4 calls:

14.0ms	(* (* n 2) PI)
105.0ms	(* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
33.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
35.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series797.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (* n 2) PI)
320.0ms	(* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
193.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
215.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify4.3s

Counts

1193 → 1193

Iterations

Iter	Nodes
done	5001
1	2820
0	1610

prune7.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
0.2b	(/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))
0.2b	(* (* n 2) PI)
1.7b	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite648.0ms

Algorithm

rewrite-expression-head

Rules

11044×	`times-frac`
8334×	`sqrt-prod`
6333×	`add-sqr-sqrt`
6330×	`*-un-lft-identity`
6328×	`add-cube-cbrt`
4141×	`unpow-prod-up`
3939×	`prod-diff`
464×	`associate-/l*`
315×	`div-inv`
101×	`sub-neg` `unpow-prod-down` `sqr-pow`
46×	`add-exp-log`
18×	`associate-/r*`
16×	`add-cbrt-cube` `div-exp`
15×	`pow1`
12×	`prod-exp`
9×	`pow-exp`
6×	`pow-unpow` `pow-prod-down`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `associate-r` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `pow-sub` `difference-of-squares` `associate-/l/`
1×	`associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 4788

Calls

4 calls:

26.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
50.0ms	(/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))
26.0ms	(* (* n 2) PI)
41.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series832.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
300.0ms	(/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))
57.0ms	(* (* n 2) PI)
197.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify13.6s

Counts

4800 → 4800

Iterations

Iter	Nodes
done	5000
0	3691

prune29.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* n 2) PI)
0.3b	(* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
1.6b	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
1.6b	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
64×	`prod-exp`
63×	`add-sqr-sqrt`
44×	`pow-unpow`
42×	`times-frac`
41×	`*-un-lft-identity`
36×	`pow-exp`
29×	`add-cube-cbrt`
21×	`pow1`
12×	`pow-to-exp` `difference-of-squares`
11×	`add-cbrt-cube`
10×	`pow-prod-down` `sqr-pow`
8×	`associate-r`
6×	`unpow-prod-down` `pow-pow` `div-sub` `associate-l` `distribute-lft-out--` `pow-sub`
5×	`swap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`pow2` `frac-times` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`

Counts

4 → 168

Calls

4 calls:

30.0ms	(* (* n 2) PI)
42.0ms	(* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
39.0ms	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
34.0ms	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))

series792.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (* n 2) PI)
257.0ms	(* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
249.0ms	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
219.0ms	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))

simplify2.6s

Counts

180 → 180

Iterations

Iter	Nodes
done	5002
2	2384
1	690
0	242

prune892.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes96.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.9s	20134×	body	80	nan
2.0s	11804×	body	80	valid
0.0ms	1×	body	160	nan