Details

sample208.0ms

Algorithm

intervals

Results

90.0ms	621×	body	80	nan
62.0ms	359×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

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)))

rewrite68.0ms

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:

26.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
24.0ms	(* n (* 2 PI))
15.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series541.0ms

Counts

3 → 9

Calls

3 calls:

313.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
42.0ms	(* n (* 2 PI))
185.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.2s

Counts

127 → 127

Iterations

Iter	Nodes
2	2014
1	644
0	267

prune514.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize33.0ms

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))

rewrite97.0ms

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:

31.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
15.0ms	(* (* 2 PI) n)
8.0ms	(/ 1 (sqrt k))
39.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series661.0ms

Counts

4 → 12

Calls

4 calls:

340.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
42.0ms	(* (* 2 PI) n)
49.0ms	(/ 1 (sqrt k))
230.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.6s

Counts

188 → 188

Iterations

Iter	Nodes
2	2604
1	923
0	345

prune777.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize53.0ms

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))

rewrite77.0ms

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×	`pow-pow` `insert-posit16` `distribute-lft-out--` `add-log-exp`
2×	`div-sub` `*-commutative` `pow-sub`
1×	`associate-*r/` `div-inv`

Counts

3 → 103

Calls

3 calls:

22.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
22.0ms	(* (* 2 PI) n)
31.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series622.0ms

Counts

3 → 9

Calls

3 calls:

373.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
48.0ms	(* (* 2 PI) n)
200.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.7s

Counts

112 → 112

Iterations

Iter	Nodes
2	2410
1	711
0	258

prune508.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize32.0ms

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)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

1314×	`sqrt-prod`
1297×	`times-frac`
559×	`add-sqr-sqrt`
556×	`*-un-lft-identity`
554×	`add-cube-cbrt`
202×	`unpow-prod-up`
101×	`sub-neg` `unpow-prod-down` `sqr-pow`
74×	`associate-/l*`
46×	`add-exp-log`
18×	`associate-/r*`
16×	`add-cbrt-cube` `div-exp`
15×	`pow1`
12×	`prod-exp` `div-inv`
9×	`pow-exp`
6×	`pow-unpow` `pow-prod-down`
4×	`cbrt-undiv` `insert-posit16` `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 → 841

Calls

4 calls:

33.0ms	(/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))
33.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
26.0ms	(* n (* 2 PI))
30.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

460.0ms	(/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))
376.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
37.0ms	(* n (* 2 PI))
178.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.7s

Counts

853 → 853

Iterations

Iter	Nodes
1	2003
0	865

prune3.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes168.0ms

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
2	16
1	16
0	13

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.6s	20592×	body	80	nan
2.3s	11910×	body	80	valid
0.0ms	1×	body	160	nan