Details

sample224.0ms

Algorithm

intervals

Results

127.0ms	645×	body	80	nan
65.0ms	365×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

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

rewrite85.0ms

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:

19.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
27.0ms	(* (* n 2) PI)
36.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series632.0ms

Counts

3 → 9

Calls

3 calls:

367.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
60.0ms	(* (* n 2) PI)
205.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify1.4s

Counts

127 → 127

Iterations

Iter	Nodes
done	2001
2	2001
1	662
0	271

prune632.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.3b	(/ 1 (sqrt k))
0.3b	(* (* 2 PI) n)
0.6b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

rewrite109.0ms

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×	`insert-posit16` `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 → 176

Calls

4 calls:

59.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
10.0ms	(/ 1 (sqrt k))
17.0ms	(* (* 2 PI) n)
18.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series695.0ms

Counts

4 → 12

Calls

4 calls:

370.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
38.0ms	(/ 1 (sqrt k))
55.0ms	(* (* 2 PI) n)
231.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.6s

Counts

188 → 188

Iterations

Iter	Nodes
done	2001
2	2001
1	930
0	345

prune772.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* n 2) PI)
0.3b	(* (* n 2) PI)
0.5b	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
0.5b	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))

rewrite98.0ms

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-r` `pow-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`insert-posit16` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

13.0ms	(* (* n 2) PI)
23.0ms	(* (* n 2) PI)
32.0ms	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
28.0ms	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))

series442.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* n 2) PI)
38.0ms	(* (* n 2) PI)
180.0ms	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
183.0ms	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))

simplify1.6s

Counts

130 → 130

Iterations

Iter	Nodes
done	2002
3	2002
2	1556
1	462
0	165

prune868.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
0.3b	(* (* n 2) PI)
0.5b	(pow (* n 2) (/ (- 1/2 (/ k 2)) 2))
0.5b	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 156

Calls

4 calls:

21.0ms	(/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
28.0ms	(* (* n 2) PI)
21.0ms	(pow (* n 2) (/ (- 1/2 (/ k 2)) 2))
16.0ms	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))

series729.0ms

Counts

4 → 12

Calls

4 calls:

361.0ms	(/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
62.0ms	(* (* n 2) PI)
107.0ms	(pow (* n 2) (/ (- 1/2 (/ k 2)) 2))
199.0ms	(pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))

simplify1.5s

Counts

168 → 168

Iterations

Iter	Nodes
done	2000
2	2000
1	986
0	370

prune1.1s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0b

regimes342.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.1s	20286×	body	80	nan
2.5s	11894×	body	80	valid
1.0ms	2×	body	160	nan