Details

sample118.0ms

Algorithm

intervals

Results

56.0ms	677×	body	80	nan
34.0ms	373×	body	80	valid

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2719
5	929
4	327
3	124
2	62
1	31
0	13

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

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)))

rewrite91.0ms

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-r` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-l` `*-commutative` `div-inv` `distribute-lft-out--` `associate-/l/`

Counts

3 → 118

Calls

3 calls:

31.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
29.0ms	(* (* n 2) PI)
24.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series609.0ms

Counts

3 → 9

Calls

3 calls:

363.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
44.0ms	(* (* n 2) PI)
202.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify2.9s

Counts

127 → 127

Iterations

Iter	Nodes
done	5008
2	2241
1	662
0	271

prune624.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
102×	`add-sqr-sqrt`
73×	`*-un-lft-identity` `add-cube-cbrt`
63×	`sqrt-prod`
58×	`associate-r`
53×	`add-exp-log`
48×	`unpow-prod-down`
32×	`unpow-prod-up`
27×	`sqr-pow`
21×	`prod-exp`
16×	`sub-neg` `pow-exp`
15×	`div-exp`
14×	`unswap-sqr`
11×	`pow-to-exp` `add-cbrt-cube`
9×	`associate-/l*`
8×	`pow1`
7×	`associate-l`
6×	`pow-unpow` `associate-/r*`
5×	`pow-sub`
4×	`insert-posit16` `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 → 236

Calls

4 calls:

24.0ms	(/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k))
45.0ms	(* (pow (* n 2) (- 1/2 (* 1/2 k))) (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k)))
5.0ms	(pow PI (- 1/2 (* 1/2 k)))
19.0ms	(pow (* n 2) (- 1/2 (* 1/2 k)))

series895.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k))
507.0ms	(* (pow (* n 2) (- 1/2 (* 1/2 k))) (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k)))
58.0ms	(pow PI (- 1/2 (* 1/2 k)))
120.0ms	(pow (* n 2) (- 1/2 (* 1/2 k)))

simplify4.1s

Counts

248 → 248

Iterations

Iter	Nodes
done	5001
2	4539
1	1223
0	429

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

139×	`add-exp-log`
90×	`add-sqr-sqrt`
87×	`prod-exp`
72×	`times-frac`
59×	`associate-r`
43×	`pow-to-exp` `unpow-prod-down` `*-un-lft-identity` `pow-exp` `add-cube-cbrt`
36×	`div-exp` `sqrt-prod`
23×	`sqr-pow`
21×	`unswap-sqr`
20×	`unpow-prod-up`
18×	`add-cbrt-cube` `associate-l`
12×	`pow-sub`
10×	`sub-neg`
7×	`cbrt-unprod`
6×	`frac-times` `pow1` `pow-unpow` `associate-*r/`
4×	`associate-*l/` `insert-posit16` `add-log-exp`
2×	`cbrt-undiv` `pow-pow` `*-commutative`
1×	`div-inv`

Counts

4 → 224

Calls

4 calls:

74.0ms	(* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k))))
68.0ms	(* (pow 2 (- 1/2 (* 1/2 k))) (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k)))
5.0ms	(pow PI (- 1/2 (* 1/2 k)))
6.0ms	(pow n (- 1/2 (* 1/2 k)))

series1.5s

Counts

4 → 12

Calls

4 calls:

777.0ms	(* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k))))
585.0ms	(* (pow 2 (- 1/2 (* 1/2 k))) (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k)))
72.0ms	(pow PI (- 1/2 (* 1/2 k)))
114.0ms	(pow n (- 1/2 (* 1/2 k)))

simplify2.7s

Counts

236 → 236

Iterations

Iter	Nodes
done	5001
1	1417
0	460

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
24×	`add-sqr-sqrt` `prod-exp`
15×	`associate-r`
14×	`unpow-prod-down` `*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube`
10×	`pow-to-exp` `associate-l` `pow-exp`
8×	`unpow-prod-up`
7×	`pow-sub`
6×	`pow1` `pow-unpow` `sqrt-prod` `unswap-sqr` `sqr-pow`
4×	`sub-neg` `associate-*l/` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`pow-pow` `*-commutative`
1×	`frac-times` `associate-*r/`

Counts

4 → 113

Calls

4 calls:

42.0ms	(* (* (pow n (- 1/2 (* 1/2 k))) (sqrt 2)) (pow PI (- 1/2 (* 1/2 k))))
18.0ms	(* (pow n (- 1/2 (* 1/2 k))) (sqrt 2))
9.0ms	(pow PI (- 1/2 (* 1/2 k)))
9.0ms	(pow n (- 1/2 (* 1/2 k)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(* (* (pow n (- 1/2 (* 1/2 k))) (sqrt 2)) (pow PI (- 1/2 (* 1/2 k))))
164.0ms	(* (pow n (- 1/2 (* 1/2 k))) (sqrt 2))
76.0ms	(pow PI (- 1/2 (* 1/2 k)))
91.0ms	(pow n (- 1/2 (* 1/2 k)))

simplify1.8s

Counts

125 → 125

Iterations

Iter	Nodes
done	5003
2	2040
1	578
0	203

prune891.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.0s	20838×	body	80	nan
2.1s	11857×	body	80	valid
0.0ms	1×	body	160	nan