Details

sample231.0ms

Algorithm

intervals

Results

113.0ms	655×	body	80	nan
86.0ms	365×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

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))
1.4b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite49.0ms

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:

19.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
13.0ms	(* n (* 2 PI))
14.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series591.0ms

Counts

3 → 9

Calls

3 calls:

337.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
65.0ms	(* n (* 2 PI))
188.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.1s

Counts

127 → 127

Iterations

Iter	Nodes
2	2014
1	644
0	267

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

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))
1.4b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

352×	`times-frac`
166×	`add-sqr-sqrt`
163×	`*-un-lft-identity`
161×	`add-cube-cbrt`
108×	`sqrt-prod`
72×	`add-exp-log`
64×	`unpow-prod-up`
54×	`associate-/r*`
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/` `div-inv` `pow-sub`
5×	`pow-to-exp`
4×	`cbrt-undiv` `insert-posit16` `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 → 343

Calls

4 calls:

22.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
19.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
13.0ms	(* n (* 2 PI))
19.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

336.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
421.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
71.0ms	(* n (* 2 PI))
182.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify6.7s

Counts

355 → 355

Iterations

Iter	Nodes
2	3999
1	1424
0	532

prune4.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (sqrt k)) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
0.2b	(/ 1 (sqrt k))
0.3b	(* n (* 2 PI))
1.4b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

1560×	`times-frac`
630×	`add-sqr-sqrt`
627×	`*-un-lft-identity`
625×	`add-cube-cbrt`
255×	`sqrt-prod`
207×	`add-exp-log`
140×	`unpow-prod-up`
138×	`div-exp`
70×	`sub-neg` `unpow-prod-down` `sqr-pow`
52×	`div-inv`
42×	`prod-exp`
39×	`pow-exp`
37×	`rec-exp` `1-exp`
32×	`associate-/r*`
25×	`associate-/l*`
24×	`associate-/r/` `pow-sub`
23×	`add-cbrt-cube`
17×	`pow1`
13×	`pow-to-exp`
9×	`cbrt-undiv`
6×	`pow-unpow` `pow-prod-down`
4×	`insert-posit16` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod` `pow-flip`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--` `inv-pow` `associate-/l/`

Counts

4 → 792

Calls

4 calls:

30.0ms	(/ (/ 1 (sqrt k)) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
5.0ms	(/ 1 (sqrt k))
15.0ms	(* n (* 2 PI))
15.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series662.0ms

Counts

4 → 12

Calls

4 calls:

360.0ms	(/ (/ 1 (sqrt k)) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
47.0ms	(/ 1 (sqrt k))
42.0ms	(* n (* 2 PI))
212.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify16.5s

Counts

804 → 804

Iterations

Iter	Nodes
1	3414
0	1060

prune10.7s

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	(* (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))
1.4b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
1.4b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

444×	`sqrt-prod`
278×	`times-frac`
253×	`add-sqr-sqrt`
111×	`*-un-lft-identity`
107×	`add-cube-cbrt`
92×	`unpow-prod-up`
81×	`swap-sqr`
54×	`sqr-pow`
52×	`associate-l`
50×	`associate-r`
46×	`sub-neg`
36×	`pow1` `unswap-sqr`
30×	`unpow-prod-down`
23×	`add-exp-log`
12×	`pow-unpow` `pow-prod-down`
11×	`add-cbrt-cube`
10×	`prod-exp`
8×	`sqrt-pow1` `pow1/2`
6×	`pow-pow` `pow-exp`
5×	`pow-prod-up`
4×	`sqrt-div` `cbrt-unprod` `insert-posit16` `div-inv` `add-log-exp` `difference-of-squares`
3×	`pow-sqr`
2×	`pow-to-exp` `*-commutative` `distribute-lft-out--` `pow-sub`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `associate-r/`

Counts

4 → 315

Calls

4 calls:

12.0ms	(* n (* 2 PI))
26.0ms	(* (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))
23.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
27.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series759.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* n (* 2 PI))
324.0ms	(* (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))
177.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
196.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.4s

Counts

327 → 327

Iterations

Iter	Nodes
2	2697
1	914
0	451

prune4.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes123.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	17
1	17
0	15

end0.0ms

sample7.7s

Algorithm

intervals

Results

3.8s	20720×	body	80	nan
2.7s	11903×	body	80	valid
1.0ms	3×	body	160	nan