Details

sample234.0ms

Algorithm

intervals

Results

127.0ms	607×	body	80	nan
75.0ms	382×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	2011
6	2011
5	929
4	327
3	124
2	62
1	31
0	13

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize44.0ms

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

rewrite94.0ms

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:

29.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
28.0ms	(* (* n 2) PI)
33.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series576.0ms

Counts

3 → 9

Calls

3 calls:

324.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
59.0ms	(* (* n 2) PI)
193.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify1.3s

Counts

127 → 127

Iterations

Iter	Nodes
done	2001
2	2001
1	662
0	271

prune848.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
0.2b	(* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))
0.5b	(pow PI (- 1/2 (/ k 2)))
0.6b	(pow (* n 2) (- 1/2 (/ k 2)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
112×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
73×	`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`
12×	`pow-unpow`
11×	`pow-to-exp` `add-cbrt-cube`
9×	`associate-/l*`
8×	`pow1`
7×	`associate-l`
6×	`associate-/r*`
5×	`pow-sub`
4×	`insert-posit16` `add-log-exp` `difference-of-squares`
3×	`pow-pow`
2×	`cbrt-undiv` `cbrt-unprod` `div-inv` `distribute-lft-out--`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 242

Calls

4 calls:

16.0ms	(/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
50.0ms	(* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))
5.0ms	(pow PI (- 1/2 (/ k 2)))
9.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

series967.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
511.0ms	(* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))
78.0ms	(pow PI (- 1/2 (/ k 2)))
154.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

simplify2.8s

Counts

254 → 254

Iterations

Iter	Nodes
done	2000
2	2000
1	1246
0	442

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt 1/2) (sqrt (/ k 2)))
0.1b	(/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k))
0.2b	(* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))
0.6b	(pow (* n 2) (- 1/2 (/ k 2)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
161×	`unpow-prod-down`
154×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
104×	`add-cube-cbrt`
99×	`sqrt-prod`
88×	`associate-r`
75×	`add-exp-log`
47×	`sqr-pow`
43×	`unpow-prod-up`
34×	`pow-exp`
31×	`prod-exp`
25×	`div-exp`
22×	`unswap-sqr`
17×	`pow-to-exp`
15×	`sub-neg`
14×	`associate-/l*`
11×	`add-cbrt-cube`
7×	`pow1` `associate-l`
6×	`pow-unpow` `associate-/r*` `add-log-exp`
4×	`insert-posit16` `pow-sub`
2×	`cbrt-undiv` `pow-pow` `cbrt-unprod` `div-inv` `distribute-lft-out` `difference-of-squares`
1×	`frac-times` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+` `distribute-lft-out--` `associate-/l/`

Counts

4 → 315

Calls

4 calls:

7.0ms	(+ (sqrt 1/2) (sqrt (/ k 2)))
15.0ms	(/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k))
42.0ms	(* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))
14.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

series9.5s

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (sqrt 1/2) (sqrt (/ k 2)))
5.0s	(/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k))
4.2s	(* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))
147.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

simplify4.1s

Counts

327 → 327

Iterations

Iter	Nodes
done	2000
1	2000
0	725

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
18×	`pow-unpow`
17×	`*-un-lft-identity`
11×	`unpow-prod-down` `add-cube-cbrt`
9×	`pow1` `add-exp-log` `sqrt-prod`
8×	`unpow-prod-up`
6×	`difference-of-squares`
5×	`sqr-pow`
4×	`sub-neg` `pow-pow` `add-cbrt-cube` `pow-exp` `insert-posit16` `pow-sub` `add-log-exp`
3×	`pow-to-exp` `rem-sqrt-square` `times-frac` `distribute-lft-out--`
1×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp`

Counts

4 → 95

Calls

4 calls:

6.0ms	(sqrt (pow PI (- 1/2 (/ k 2))))
10.0ms	(pow PI (- 1/2 (/ k 2)))
7.0ms	(pow PI (- 1/2 (/ k 2)))
8.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(sqrt (pow PI (- 1/2 (/ k 2))))
68.0ms	(pow PI (- 1/2 (/ k 2)))
73.0ms	(pow PI (- 1/2 (/ k 2)))
140.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

simplify1.5s

Counts

107 → 107

Iterations

Iter	Nodes
done	2007
3	2007
2	1336
1	415
0	157

prune726.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes270.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.2s	20747×	body	80	nan
2.8s	11976×	body	80	valid
0.0ms	1×	body	160	nan