Details

sample220.0ms

Algorithm

intervals

Results

99.0ms	621×	body	80	nan
89.0ms	359×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2026
6	2026
5	970
4	328
3	124
2	62
1	31
0	13

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

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

rewrite89.0ms

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-l` `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-r` `*-commutative` `distribute-lft-out--` `associate-/l/`

Counts

3 → 436

Calls

3 calls:

31.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
25.0ms	(* n (* 2 PI))
16.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series524.0ms

Counts

3 → 9

Calls

3 calls:

298.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
44.0ms	(* n (* 2 PI))
181.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify2.2s

Counts

445 → 445

Iterations

Iter	Nodes
done	2001
2	2001
1	1526
0	695

prune6.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize48.0ms

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

rewrite144.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 184

Calls

4 calls:

63.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
35.0ms	(* (* 2 PI) n)
10.0ms	(/ 1 (sqrt k))
32.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series671.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
44.0ms	(* (* 2 PI) n)
45.0ms	(/ 1 (sqrt k))
258.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.4s

Counts

196 → 196

Iterations

Iter	Nodes
done	2008
2	2008
1	953
0	353

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
33×	`add-sqr-sqrt`
30×	`prod-exp`
26×	`*-un-lft-identity`
22×	`pow-unpow`
18×	`times-frac`
17×	`pow-exp` `add-cube-cbrt`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`pow-to-exp`
8×	`associate-r` `associate-l` `sqr-pow`
7×	`unpow-prod-down`
6×	`pow-prod-down` `difference-of-squares` `unswap-sqr`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `pow-pow` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
2×	`div-sub` `*-commutative` `pow-sub`
1×	`associate-*r/` `div-inv`

Counts

3 → 109

Calls

3 calls:

23.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
26.0ms	(* (* 2 PI) n)
15.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series930.0ms

Counts

3 → 9

Calls

3 calls:

326.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
395.0ms	(* (* 2 PI) n)
208.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.2s

Counts

118 → 118

Iterations

Iter	Nodes
done	2000
2	2000
1	732
0	264

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite515.0ms

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-l` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `pow-sub` `difference-of-squares` `associate-/l/`
1×	`associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 4788

Calls

4 calls:

42.0ms	(/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))
16.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
19.0ms	(* n (* 2 PI))
36.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series942.0ms

Counts

4 → 12

Calls

4 calls:

349.0ms	(/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))
323.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
48.0ms	(* n (* 2 PI))
221.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify12.5s

Counts

4800 → 4800

Iterations

Iter	Nodes
done	3687
0	3687

prune1.7m

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes188.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	13

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.9s	20592×	body	80	nan
2.1s	11910×	body	80	valid
0.0ms	1×	body	160	nan