Details

sample97.0ms

Algorithm

intervals

Results

42.0ms	638×	body	80	nan
29.0ms	386×	body	80	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2753
5	970
4	328
3	124
2	62
1	31
0	13

prune21.0ms

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))
0.2b	(* (* n 2) PI)
0.9b	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite112.0ms

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-r` `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-l` `*-commutative` `distribute-lft-out--` `associate-/l/`

Counts

3 → 436

Calls

3 calls:

33.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
21.0ms	(* (* n 2) PI)
27.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series575.0ms

Counts

3 → 9

Calls

3 calls:

333.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
60.0ms	(* (* n 2) PI)
182.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify3.5s

Counts

445 → 445

Iterations

Iter	Nodes
done	5000
2	4377
1	1539
0	699

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize48.0ms

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

rewrite174.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 184

Calls

4 calls:

72.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
33.0ms	(* (* 2 PI) n)
14.0ms	(/ 1 (sqrt k))
48.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series621.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
53.0ms	(* (* 2 PI) n)
44.0ms	(/ 1 (sqrt k))
208.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify2.4s

Counts

196 → 196

Iterations

Iter	Nodes
done	5003
2	2935
1	953
0	353

prune905.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
0.2b	(/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
0.5b	(pow PI (- 1/2 (/ k 2)))
0.8b	(pow (* n 2) (- 1/2 (/ k 2)))

rewrite4.3s

Algorithm

rewrite-expression-head

Rules

43099×	`times-frac`
25436×	`add-sqr-sqrt`
25430×	`*-un-lft-identity`
25426×	`add-cube-cbrt`
23985×	`unpow-prod-up`
22815×	`prod-diff`
6915×	`sqrt-prod`
1804×	`div-inv`
1165×	`unpow-prod-down`
585×	`sub-neg` `sqr-pow`
341×	`associate-/r*`
53×	`add-exp-log`
52×	`associate-/l*`
51×	`pow-sub`
49×	`associate-/r/`
31×	`div-exp`
16×	`pow-exp`
12×	`pow-unpow`
11×	`pow-to-exp` `add-cbrt-cube`
8×	`pow1`
5×	`prod-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-pow`
2×	`clear-num` `frac-2neg` `distribute-lft-out--`
1×	`pow-prod-down` `associate-/l/`

Counts

4 → 14340

Calls

4 calls:

28.0ms	(/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
406.0ms	(/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
16.0ms	(pow PI (- 1/2 (/ k 2)))
33.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

295.0ms	(/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
533.0ms	(/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
70.0ms	(pow PI (- 1/2 (/ k 2)))
128.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

simplify1.3m

Counts

14352 → 14352

Iterations

Iter	Nodes
done	13534
0	13534

prune2.2m

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI 1/2)))
0.3b	(/ (sqrt k) (pow PI 1/2))
0.8b	(pow n (- 1/2 (/ k 2)))
1.0b	(pow PI 1/2)

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

5605×	`times-frac`
3092×	`add-sqr-sqrt`
3089×	`*-un-lft-identity`
3087×	`add-cube-cbrt`
1968×	`unpow-prod-up`
1872×	`prod-diff`
1053×	`sqrt-prod`
1050×	`unpow-prod-down`
350×	`sqr-pow`
195×	`div-inv`
54×	`associate-/l*`
53×	`associate-/r*`
48×	`sub-neg`
37×	`add-exp-log`
24×	`div-exp`
11×	`add-cbrt-cube`
10×	`pow-to-exp` `pow-exp`
9×	`pow-unpow`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `pow-pow` `frac-2neg` `unpow1/2` `pow-sub` `difference-of-squares`
1×	`sqrt-undiv` `associate-/r/` `distribute-lft-out--` `associate-/l/`

Counts

4 → 2490

Calls

4 calls:

76.0ms	(/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI 1/2)))
9.0ms	(/ (sqrt k) (pow PI 1/2))
13.0ms	(pow n (- 1/2 (/ k 2)))
2.0ms	(pow PI 1/2)

series303.0ms

Counts

4 → 10

Calls

4 calls:

158.0ms	(/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI 1/2)))
81.0ms	(/ (sqrt k) (pow PI 1/2))
64.0ms	(pow n (- 1/2 (/ k 2)))
0.0ms	(pow PI 1/2)

simplify4.2s

Counts

2500 → 2500

Iterations

Iter	Nodes
done	5001
0	2889

prune13.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes85.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	16

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.2s	20923×	body	80	nan
1.2s	11902×	body	80	valid