Details

sample216.0ms

Algorithm

intervals

Results

104.0ms	673×	body	80	nan
79.0ms	393×	body	80	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
6	2053
5	821
4	322
3	123
2	60
1	29
0	13

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
0.3b	(* PI (* n 2))
0.7b	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

rewrite92.0ms

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:

32.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
23.0ms	(* PI (* n 2))
16.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

series603.0ms

Counts

3 → 9

Calls

3 calls:

368.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
61.0ms	(* PI (* n 2))
174.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

simplify3.3s

Counts

445 → 445

Iterations

Iter	Nodes
2	4287
1	1515
0	698

prune6.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
0.2b	(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
0.3b	(* PI (* n 2))
0.7b	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

3088×	`times-frac`
1878×	`add-sqr-sqrt`
1875×	`*-un-lft-identity`
1873×	`add-cube-cbrt`
1312×	`unpow-prod-up`
1248×	`prod-diff`
693×	`sqrt-prod`
327×	`associate-/r*`
102×	`div-inv`
72×	`add-exp-log`
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/` `pow-sub`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `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 → 1599

Calls

4 calls:

44.0ms	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
31.0ms	(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
29.0ms	(* PI (* n 2))
33.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

series970.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
375.0ms	(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
38.0ms	(* PI (* n 2))
228.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

simplify3.0m

Counts

1611 → 1611

Iterations

Iter	Nodes
1	4705
0	1731

prune20.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow PI (- 1/2 (* 1/2 k))) (/ (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt k)))
0.2b	(/ (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt k))
0.5b	(pow PI (- 1/2 (* 1/2 k)))
0.6b	(pow (* 2 n) (- 1/2 (* 1/2 k)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
112×	`add-sqr-sqrt`
81×	`*-un-lft-identity` `add-cube-cbrt`
80×	`unpow-prod-up`
69×	`sqrt-prod`
64×	`associate-r`
53×	`add-exp-log`
48×	`prod-diff`
27×	`sqr-pow`
25×	`unpow-prod-down`
20×	`prod-exp`
16×	`sub-neg` `div-exp` `pow-exp`
15×	`unswap-sqr`
12×	`associate-l`
11×	`pow-to-exp` `add-cbrt-cube`
10×	`associate-/l*`
8×	`pow1`
6×	`pow-unpow` `associate-/r*`
5×	`pow-sub`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow`
2×	`cbrt-undiv` `cbrt-unprod` `div-inv`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 269

Calls

4 calls:

19.0ms	(* (pow PI (- 1/2 (* 1/2 k))) (/ (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt k)))
13.0ms	(/ (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt k))
3.0ms	(pow PI (- 1/2 (* 1/2 k)))
6.0ms	(pow (* 2 n) (- 1/2 (* 1/2 k)))

series637.0ms

Counts

4 → 12

Calls

4 calls:

354.0ms	(* (pow PI (- 1/2 (* 1/2 k))) (/ (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt k)))
151.0ms	(/ (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt k))
44.0ms	(pow PI (- 1/2 (* 1/2 k)))
88.0ms	(pow (* 2 n) (- 1/2 (* 1/2 k)))

simplify1.7s

Counts

281 → 281

Iterations

Iter	Nodes
2	4112
1	1240
0	449

prune2.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow n (- 1/2 (* 1/2 k))) (sqrt k))
0.2b	(* (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (/ (pow n (- 1/2 (* 1/2 k))) (sqrt k)))
0.5b	(pow PI (- 1/2 (* 1/2 k)))
0.6b	(pow n (- 1/2 (* 1/2 k)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-exp-log`
100×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
76×	`associate-r` `prod-exp`
75×	`unpow-prod-up` `sqrt-prod`
45×	`unpow-prod-down` `prod-diff`
37×	`pow-to-exp` `pow-exp`
33×	`div-exp`
18×	`add-cbrt-cube`
15×	`sub-neg` `sqr-pow`
12×	`associate-/l*`
11×	`pow-sub`
8×	`pow1`
6×	`pow-unpow` `associate-/r*` `cbrt-unprod`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-*r/`
2×	`pow-pow` `div-inv`
1×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 300

Calls

4 calls:

8.0ms	(/ (pow n (- 1/2 (* 1/2 k))) (sqrt k))
37.0ms	(* (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (/ (pow n (- 1/2 (* 1/2 k))) (sqrt k)))
4.0ms	(pow PI (- 1/2 (* 1/2 k)))
4.0ms	(pow n (- 1/2 (* 1/2 k)))

series792.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (pow n (- 1/2 (* 1/2 k))) (sqrt k))
581.0ms	(* (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (/ (pow n (- 1/2 (* 1/2 k))) (sqrt k)))
42.0ms	(pow PI (- 1/2 (* 1/2 k)))
64.0ms	(pow n (- 1/2 (* 1/2 k)))

simplify1.6s

Counts

312 → 312

Iterations

Iter	Nodes
2	4750
1	1395
0	466

prune2.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes87.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	16
1	16
0	14

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.6s	20948×	body	80	nan
1.4s	11935×	body	80	valid
0.0ms	1×	body	160	nan