Details

sample240.0ms

Algorithm

intervals

Results

135.0ms	645×	body	80	nan
73.0ms	365×	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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
0.3b	(* n (* 2 PI))
0.6b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite82.0ms

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:

17.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
25.0ms	(* n (* 2 PI))
18.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series558.0ms

Counts

3 → 9

Calls

3 calls:

337.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
42.0ms	(* n (* 2 PI))
179.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify2.3s

Counts

445 → 445

Iterations

Iter	Nodes
done	2001
2	2001
1	1526
0	695

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.3b	(/ 1 (sqrt k))
0.3b	(* (* 2 PI) n)
0.6b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

rewrite143.0ms

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:

66.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
11.0ms	(/ 1 (sqrt k))
29.0ms	(* (* 2 PI) n)
32.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series625.0ms

Counts

4 → 12

Calls

4 calls:

337.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
45.0ms	(/ 1 (sqrt k))
40.0ms	(* (* 2 PI) n)
203.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.3s

Counts

196 → 196

Iterations

Iter	Nodes
done	2004
2	2004
1	952
0	353

prune858.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.3b	(* (* 2 PI) n)
0.6b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

rewrite78.0ms

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:

44.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
15.0ms	(* (* 2 PI) n)
16.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series561.0ms

Counts

3 → 9

Calls

3 calls:

336.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
62.0ms	(* (* 2 PI) n)
163.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.2s

Counts

118 → 118

Iterations

Iter	Nodes
done	2000
2	2000
1	732
0	264

prune584.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
0.2b	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
0.3b	(* n (* 2 PI))
0.6b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

3088×	`times-frac`
1878×	`add-sqr-sqrt`
1875×	`*-un-lft-identity`
1873×	`add-cube-cbrt`
1312×	`unpow-prod-up`
1248×	`prod-diff`
693×	`sqrt-prod`
327×	`associate-/r*`
102×	`div-inv`
72×	`add-exp-log`
32×	`sub-neg` `unpow-prod-down` `div-exp` `sqr-pow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
6×	`rec-exp` `pow-unpow` `1-exp` `pow-prod-down` `associate-/r/` `pow-sub`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`associate-r` `*-commutative` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 1599

Calls

4 calls:

49.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
26.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
27.0ms	(* n (* 2 PI))
36.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series991.0ms

Counts

4 → 12

Calls

4 calls:

394.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
341.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
43.0ms	(* n (* 2 PI))
214.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify3.7s

Counts

1611 → 1611

Iterations

Iter	Nodes
done	2002
1	2002
0	1728

prune11.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes171.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	13

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.6s	20286×	body	80	nan
2.4s	11894×	body	80	valid
1.0ms	2×	body	160	nan