Details

sample148.0ms

Algorithm

intervals

Results

66.0ms	618×	body	80	nan
46.0ms	354×	body	80	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2719
5	929
4	327
3	124
2	62
1	31
0	13

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

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)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt`
26×	`add-exp-log`
24×	`sqrt-prod`
16×	`unpow-prod-up`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sub-neg` `unpow-prod-down` `sqr-pow`
7×	`associate-/l*`
6×	`pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp`
3×	`pow-pow` `associate-r` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-l` `*-commutative` `div-inv` `distribute-lft-out--` `associate-/l/`

Counts

3 → 118

Calls

3 calls:

24.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
28.0ms	(* (* n 2) PI)
34.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series579.0ms

Counts

3 → 9

Calls

3 calls:

324.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
36.0ms	(* (* n 2) PI)
219.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify2.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5008
2	2241
1	662
0	271

prune637.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt` `add-exp-log`
62×	`times-frac`
57×	`*-un-lft-identity`
44×	`add-cube-cbrt`
38×	`prod-exp`
25×	`sqrt-prod`
23×	`associate-l`
22×	`pow-unpow`
17×	`pow1`
16×	`add-cbrt-cube`
15×	`pow-exp`
12×	`div-exp`
10×	`unswap-sqr`
8×	`associate-r`
7×	`sqr-pow`
6×	`rec-exp` `associate-/r*` `1-exp` `pow-prod-down` `difference-of-squares`
5×	`pow-to-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`pow-pow` `div-sub` `div-inv` `pow-flip` `associate-/l*` `distribute-lft-out--` `pow-sub`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `inv-pow`

Counts

4 → 176

Calls

4 calls:

59.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
34.0ms	(* (* 2 PI) n)
10.0ms	(/ 1 (sqrt k))
32.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series722.0ms

Counts

4 → 12

Calls

4 calls:

385.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
64.0ms	(* (* 2 PI) n)
49.0ms	(/ 1 (sqrt k))
223.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify2.3s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
2	2858
1	931
0	345

prune879.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize33.0ms

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)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

444×	`sqrt-prod`
278×	`times-frac`
253×	`add-sqr-sqrt`
111×	`*-un-lft-identity`
107×	`add-cube-cbrt`
92×	`unpow-prod-up`
81×	`swap-sqr`
54×	`sqr-pow`
52×	`associate-r`
50×	`associate-l`
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×	`sqrt-div` `cbrt-unprod` `insert-posit16` `div-inv` `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 → 315

Calls

4 calls:

15.0ms	(* (* n 2) PI)
40.0ms	(* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
20.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
25.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series765.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* n 2) PI)
328.0ms	(* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
181.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
215.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify2.6s

Counts

327 → 327

Iterations

Iter	Nodes
done	5001
2	3062
1	946
0	455

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize88.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
36×	`sqrt-prod`
33×	`*-un-lft-identity`
29×	`times-frac` `add-cube-cbrt`
25×	`add-exp-log`
24×	`pow1`
12×	`pow-unpow`
11×	`add-cbrt-cube`
9×	`associate-/r*` `pow-prod-down` `prod-exp`
6×	`pow-pow` `pow-exp`
5×	`pow-flip`
4×	`unpow-prod-up` `sqrt-pow1` `insert-posit16` `add-log-exp` `difference-of-squares`
3×	`associate-r` `cbrt-unprod` `associate-/l*`
2×	`pow-to-exp` `sub-neg` `unpow-prod-down` `pow1/2` `div-exp` `distribute-lft-out--` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-l` `*-commutative` `div-inv` `inv-pow`

Counts

4 → 131

Calls

4 calls:

24.0ms	(* (* n 2) PI)
12.0ms	(/ 1 (sqrt (sqrt k)))
34.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
32.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series727.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* n 2) PI)
264.0ms	(/ 1 (sqrt (sqrt k)))
230.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
176.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify1.6s

Counts

143 → 143

Iterations

Iter	Nodes
done	5004
2	1700
1	540
0	232

prune877.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes344.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	18
1	18
0	13

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.3s	20134×	body	80	nan
1.9s	11804×	body	80	valid
0.0ms	1×	body	160	nan