Details

sample242.0ms

Algorithm

intervals

Results

137.0ms	655×	body	80	nan
71.0ms	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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

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)))

rewrite83.0ms

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:

19.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
13.0ms	(* n (* 2 PI))
30.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series553.0ms

Counts

3 → 9

Calls

3 calls:

301.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
65.0ms	(* n (* 2 PI))
186.0ms	(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

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* n (* 2 PI))
0.3b	(* n (* 2 PI))
1.3b	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
1.3b	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

rewrite116.0ms

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:

25.0ms	(* n (* 2 PI))
31.0ms	(* n (* 2 PI))
30.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
27.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

series528.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* n (* 2 PI))
50.0ms	(* n (* 2 PI))
225.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
209.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

simplify1.6s

Counts

138 → 138

Iterations

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

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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:

12.0ms	(* n (* 2 PI))
15.0ms	(* n (* 2 PI))
16.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
22.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* n (* 2 PI))
41.0ms	(* n (* 2 PI))
194.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
194.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.3s

Counts

188 → 188

Iterations

Iter	Nodes
done	2000
2	2000
1	900
0	292

prune3.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize59.0ms

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)))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

2180×	`times-frac`
2082×	`sqrt-prod`
1741×	`add-sqr-sqrt`
1443×	`*-un-lft-identity`
1439×	`add-cube-cbrt`
1262×	`unpow-prod-up`
1170×	`prod-diff`
393×	`swap-sqr`
286×	`associate-l`
284×	`associate-r`
94×	`div-inv`
54×	`sqr-pow`
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×	`expm1-log1p-u` `sqrt-div` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `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 → 1181

Calls

4 calls:

13.0ms	(* n (* 2 PI))
115.0ms	(* (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))
15.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
29.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series810.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* n (* 2 PI))
342.0ms	(* (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))
194.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
230.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify5.1s

Counts

1193 → 1193

Iterations

Iter	Nodes
done	2001
1	2001
0	1606

prune23.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	21
1	21
0	16

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.4s	20720×	body	80	nan
2.6s	11903×	body	80	valid
1.0ms	3×	body	160	nan