Details

sample216.0ms

Algorithm

intervals

Results

115.0ms	619×	body	80	nan
68.0ms	386×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
6	2083
5	817
4	322
3	123
2	60
1	29
0	13

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize51.0ms

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))
1.1b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite87.0ms

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-l` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `div-inv` `distribute-lft-out--` `associate-/l/`

Counts

3 → 118

Calls

3 calls:

25.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
28.0ms	(* n (* 2 PI))
31.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series590.0ms

Counts

3 → 9

Calls

3 calls:

321.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
44.0ms	(* n (* 2 PI))
224.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.1s

Counts

127 → 127

Iterations

Iter	Nodes
2	2014
1	644
0	267

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k)))
0.2b	(/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
0.5b	(pow (* 2 PI) (- 1/2 (/ k 2)))
0.8b	(pow n (- 1/2 (/ k 2)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac`
94×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
53×	`add-exp-log` `add-cube-cbrt`
51×	`sqrt-prod`
46×	`associate-r`
32×	`unpow-prod-up`
27×	`sqr-pow`
25×	`unpow-prod-down`
20×	`prod-exp`
16×	`sub-neg` `div-exp` `pow-exp`
15×	`unswap-sqr`
12×	`pow-unpow`
11×	`pow-to-exp` `add-cbrt-cube`
9×	`associate-l`
8×	`pow1`
7×	`associate-/l*`
6×	`associate-/r*`
5×	`pow-sub`
4×	`insert-posit16` `add-log-exp` `difference-of-squares`
3×	`pow-pow`
2×	`cbrt-undiv` `cbrt-unprod` `div-inv` `distribute-lft-out--`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 219

Calls

4 calls:

28.0ms	(* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k)))
10.0ms	(/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
10.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
12.0ms	(pow n (- 1/2 (/ k 2)))

series952.0ms

Counts

4 → 12

Calls

4 calls:

446.0ms	(* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k)))
320.0ms	(/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
106.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
81.0ms	(pow n (- 1/2 (/ k 2)))

simplify1.9s

Counts

231 → 231

Iterations

Iter	Nodes
2	3572
1	1053
0	387

prune3.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))))
0.5b	(pow (* 2 PI) (- 1/2 (/ k 2)))
0.5b	(pow (* 2 PI) (- 1/2 (/ k 2)))
0.8b	(pow n (- 1/2 (/ k 2)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

1370×	`times-frac`
1280×	`sqrt-prod`
674×	`add-sqr-sqrt`
655×	`associate-r`
477×	`*-un-lft-identity`
471×	`add-cube-cbrt`
258×	`unpow-prod-up`
190×	`sqr-pow`
155×	`unpow-prod-down`
129×	`sub-neg`
66×	`unswap-sqr`
35×	`add-exp-log`
18×	`pow-unpow`
15×	`pow-sub`
13×	`add-cbrt-cube`
11×	`pow1` `prod-exp` `associate-/r/` `div-inv`
10×	`sqrt-div`
9×	`div-exp` `associate-l`
8×	`pow-exp`
6×	`pow-to-exp` `difference-of-squares`
5×	`pow-pow`
4×	`insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
2×	`pow-prod-down`
1×	`frac-times` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 826

Calls

4 calls:

72.0ms	(* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))))
17.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
18.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
12.0ms	(pow n (- 1/2 (/ k 2)))

series760.0ms

Counts

4 → 12

Calls

4 calls:

516.0ms	(* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))))
89.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
78.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
76.0ms	(pow n (- 1/2 (/ k 2)))

simplify4.9s

Counts

838 → 838

Iterations

Iter	Nodes
1	3394
0	1042

prune15.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))))
0.5b	(pow PI (- 1/2 (/ k 2)))
0.5b	(pow (* 2 PI) (- 1/2 (/ k 2)))
0.8b	(pow n (- 1/2 (/ k 2)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

1503×	`times-frac`
1449×	`sqrt-prod`
785×	`associate-r`
616×	`add-sqr-sqrt`
607×	`*-un-lft-identity`
601×	`add-cube-cbrt`
280×	`unpow-prod-up`
274×	`unpow-prod-down`
140×	`sub-neg` `sqr-pow`
51×	`add-exp-log`
25×	`add-cbrt-cube`
23×	`pow-sub`
22×	`prod-exp`
18×	`pow-unpow`
16×	`sqrt-div`
13×	`associate-/r/` `div-inv`
12×	`div-exp`
11×	`pow1`
9×	`cbrt-unprod`
7×	`pow-exp`
6×	`pow-to-exp` `cbrt-undiv` `difference-of-squares`
5×	`frac-times` `associate-*l/`
4×	`pow-pow` `insert-posit16` `add-log-exp`
3×	`associate-*r/` `distribute-lft-out--`
2×	`pow-prod-down`
1×	`associate-l` `*-commutative`

Counts

4 → 893

Calls

4 calls:

96.0ms	(* (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))))
10.0ms	(pow PI (- 1/2 (/ k 2)))
10.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
13.0ms	(pow n (- 1/2 (/ k 2)))

series2.1s

Counts

4 → 12

Calls

4 calls:

1.8s	(* (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))))
61.0ms	(pow PI (- 1/2 (/ k 2)))
77.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
92.0ms	(pow n (- 1/2 (/ k 2)))

simplify10.4s

Counts

905 → 905

Iterations

Iter	Nodes
1	5021
0	1288

prune20.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes156.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	23
1	23
0	20

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.7s	20785×	body	80	nan
2.6s	11867×	body	80	valid
1.0ms	3×	body	160	nan