Details

sample293.0ms

Algorithm

intervals

Results

162.0ms	744×	body	80	nan
86.0ms	383×	body	80	valid

simplify2.9s

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: 0.2b

localize27.0ms

Local error

Found 3 expressions with local error:

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

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:

32.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
23.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
27.0ms	(* (* n 2) PI)

series613.0ms

Counts

3 → 9

Calls

3 calls:

199.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
365.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
49.0ms	(* (* n 2) PI)

simplify2.7s

Counts

127 → 127

Iterations

Iter	Nodes
done	5004
2	2234
1	660
0	271

prune618.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

252×	`sqrt-prod`
234×	`times-frac`
225×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
92×	`add-cube-cbrt`
70×	`associate-r`
49×	`unswap-sqr`
44×	`sqr-pow`
36×	`associate-l`
33×	`add-exp-log`
32×	`unpow-prod-up`
28×	`add-cbrt-cube`
16×	`pow1` `sub-neg` `unpow-prod-down`
12×	`prod-exp`
10×	`cbrt-unprod` `associate-/l*`
8×	`div-exp`
7×	`pow-prod-down`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`insert-posit16` `add-log-exp`
3×	`*-commutative` `div-inv`
2×	`1-exp`
1×	`frac-times` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-div` `associate-l/` `associate-r/` `pow-sub` `associate-/l/`

Counts

4 → 299

Calls

4 calls:

14.0ms	(/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
51.0ms	(* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))
28.0ms	(* (* n 2) PI)
29.0ms	(* (* n 2) PI)

series760.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
329.0ms	(* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))
35.0ms	(* (* n 2) PI)
54.0ms	(* (* n 2) PI)

simplify3.8s

Counts

311 → 311

Iterations

Iter	Nodes
done	5003
2	3408
1	1336
0	448

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

2118×	`times-frac`
2010×	`sqrt-prod`
1333×	`add-sqr-sqrt`
778×	`associate-r`
742×	`*-un-lft-identity`
656×	`add-cube-cbrt`
326×	`unpow-prod-down`
309×	`sqr-pow`
296×	`unpow-prod-up`
196×	`unswap-sqr`
148×	`sub-neg`
42×	`add-exp-log`
35×	`associate-l`
32×	`add-cbrt-cube`
16×	`div-exp`
13×	`div-inv`
12×	`pow1` `associate-/r*` `prod-exp` `associate-/r/` `pow-sub`
11×	`sqrt-div`
10×	`cbrt-undiv`
9×	`cbrt-unprod`
6×	`pow-unpow` `associate-/l*`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`1-exp`
2×	`*-commutative` `difference-of-squares`
1×	`frac-times` `pow-to-exp` `sqrt-undiv` `clear-num` `pow-pow` `frac-2neg` `associate-l/` `pow-exp` `associate-r/` `distribute-lft-out--`

Counts

4 → 1181

Calls

4 calls:

10.0ms	(/ (sqrt k) (sqrt (pow PI (- 1/2 (/ k 2)))))
54.0ms	(* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow PI (- 1/2 (/ k 2)))))))
14.0ms	(* (* n 2) PI)
6.0ms	(pow PI (- 1/2 (/ k 2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (sqrt k) (sqrt (pow PI (- 1/2 (/ k 2)))))
1000.0ms	(* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow PI (- 1/2 (/ k 2)))))))
45.0ms	(* (* n 2) PI)
67.0ms	(pow PI (- 1/2 (/ k 2)))

simplify24.6s

Counts

1193 → 1193

Iterations

Iter	Nodes
done	5000
0	1555

prune7.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

196×	`sqrt-prod`
139×	`times-frac`
130×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
78×	`add-cube-cbrt`
67×	`associate-r`
30×	`unpow-prod-up`
28×	`sqr-pow`
21×	`unswap-sqr`
17×	`unpow-prod-down` `add-exp-log`
16×	`add-cbrt-cube`
15×	`sub-neg`
12×	`pow1`
11×	`associate-l`
10×	`associate-/l*`
6×	`pow-unpow` `associate-/r*`
5×	`prod-exp` `cbrt-unprod`
4×	`pow-prod-down` `insert-posit16` `pow-sub` `add-log-exp`
3×	`sqrt-div`
2×	`cbrt-undiv` `sqrt-undiv` `div-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`frac-times` `pow-to-exp` `clear-num` `pow-pow` `frac-2neg` `sqrt-unprod` `associate-l/` `pow-exp` `associate-r/` `distribute-lft-out--` `associate-/l/`

Counts

4 → 247

Calls

4 calls:

32.0ms	(* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)))
17.0ms	(/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))
28.0ms	(* (* n 2) PI)
12.0ms	(pow PI (- 1/2 (/ k 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

701.0ms	(* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)))
244.0ms	(/ (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))
56.0ms	(* (* n 2) PI)
74.0ms	(pow PI (- 1/2 (/ k 2)))

simplify4.9s

Counts

259 → 259

Iterations

Iter	Nodes
done	5001
2	4755
1	1430
0	522

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes156.0ms

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	23
1	23
0	19

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.6s	20633×	body	80	nan
2.4s	11932×	body	80	valid
2.0ms	4×	body	160	nan