Details

sample260.0ms

Algorithm

intervals

Results

141.0ms	626×	body	80	nan
82.0ms	393×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2026
6	2026
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

localize21.0ms

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))
0.9b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite87.0ms

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:

26.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
27.0ms	(* n (* 2 PI))
22.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series560.0ms

Counts

3 → 9

Calls

3 calls:

307.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
49.0ms	(* n (* 2 PI))
204.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify2.1s

Counts

445 → 445

Iterations

Iter	Nodes
done	2001
2	2001
1	1526
0	695

prune7.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize35.0ms

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))
0.9b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite230.0ms

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:

44.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
14.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
17.0ms	(* n (* 2 PI))
30.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series955.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
365.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
69.0ms	(* n (* 2 PI))
203.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify3.9s

Counts

1611 → 1611

Iterations

Iter	Nodes
done	2002
1	2002
0	1728

prune28.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* n (* 2 PI))
0.3b	(* n (* 2 PI))
0.9b	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
0.9b	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
44×	`pow-unpow`
42×	`times-frac`
38×	`*-un-lft-identity`
26×	`pow1` `add-exp-log` `add-cube-cbrt`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `difference-of-squares`
6×	`pow-pow` `associate-l` `pow-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-r` `*-commutative` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 126

Calls

4 calls:

13.0ms	(* n (* 2 PI))
24.0ms	(* n (* 2 PI))
21.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
16.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

series500.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* n (* 2 PI))
58.0ms	(* n (* 2 PI))
186.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
209.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

simplify1.4s

Counts

138 → 138

Iterations

Iter	Nodes
done	2012
3	2012
2	1480
1	455
0	165

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* n (* 2 PI))
0.3b	(* n (* 2 PI))
0.9b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
0.9b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
82×	`unpow-prod-up`
80×	`*-un-lft-identity`
78×	`prod-diff`
76×	`add-cube-cbrt`
56×	`times-frac`
26×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
12×	`pow-unpow` `pow-prod-down` `prod-exp`
6×	`pow-pow` `associate-l` `pow-exp` `cbrt-unprod` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
2×	`pow-to-exp` `sub-neg` `unpow-prod-down` `associate-r` `*-commutative` `distribute-lft-out--` `pow-sub` `sqr-pow`

Counts

4 → 176

Calls

4 calls:

27.0ms	(* n (* 2 PI))
19.0ms	(* n (* 2 PI))
17.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
34.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* n (* 2 PI))
46.0ms	(* n (* 2 PI))
217.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
218.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.0s

Counts

188 → 188

Iterations

Iter	Nodes
done	2000
2	2000
1	900
0	292

prune3.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes114.0ms

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	14

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.8s	21126×	body	80	nan
2.4s	11926×	body	80	valid
0.0ms	1×	body	160	nan