Details

sample162.0ms

Algorithm

intervals

Results

65.0ms	386×	body	80	valid
63.0ms	638×	body	80	nan

simplify2.9s

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

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)))

rewrite84.0ms

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:

18.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
30.0ms	(* (* n 2) PI)
33.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series550.0ms

Counts

3 → 9

Calls

3 calls:

332.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
39.0ms	(* (* n 2) PI)
179.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify2.6s

Counts

127 → 127

Iterations

Iter	Nodes
done	5008
2	2241
1	662
0	271

prune696.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
0.2b	(* (* n 2) PI)
0.3b	(/ 1 (sqrt k))
0.9b	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-exp-log`
59×	`add-sqr-sqrt`
45×	`times-frac`
41×	`*-un-lft-identity`
38×	`prod-exp`
35×	`add-cube-cbrt`
25×	`associate-r` `sqrt-prod`
17×	`pow1`
16×	`add-cbrt-cube`
15×	`pow-exp`
12×	`div-exp`
10×	`unswap-sqr`
8×	`associate-l`
7×	`sqr-pow`
6×	`rec-exp` `pow-unpow` `associate-/r*` `1-exp` `pow-prod-down`
5×	`pow-to-exp` `cbrt-unprod`
4×	`unpow-prod-up` `insert-posit16` `add-log-exp`
3×	`pow-pow` `pow-flip` `associate-/l*` `pow-sub`
2×	`cbrt-undiv` `sub-neg` `unpow-prod-down` `*-commutative` `div-inv` `difference-of-squares`
1×	`frac-times` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `un-div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 165

Calls

4 calls:

36.0ms	(* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
33.0ms	(* (* n 2) PI)
6.0ms	(/ 1 (sqrt k))
24.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series646.0ms

Counts

4 → 12

Calls

4 calls:

346.0ms	(* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
52.0ms	(* (* n 2) PI)
42.0ms	(/ 1 (sqrt k))
205.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify2.4s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
2	2908
1	868
0	325

prune751.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
0.2b	(/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
0.5b	(pow PI (- 1/2 (/ k 2)))
0.8b	(pow (* n 2) (- 1/2 (/ k 2)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

901×	`times-frac`
359×	`add-sqr-sqrt`
353×	`*-un-lft-identity`
349×	`add-cube-cbrt`
246×	`sqrt-prod`
234×	`unpow-prod-up`
229×	`unpow-prod-down`
117×	`sub-neg` `sqr-pow`
68×	`associate-/r*`
53×	`add-exp-log`
31×	`div-exp`
16×	`pow-exp`
13×	`associate-/l*`
12×	`pow-unpow` `pow-sub`
11×	`pow-to-exp` `add-cbrt-cube`
10×	`associate-/r/` `div-inv`
8×	`pow1`
5×	`prod-exp`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp` `difference-of-squares`
3×	`pow-pow`
2×	`clear-num` `frac-2neg` `distribute-lft-out--`
1×	`pow-prod-down` `associate-/l/`

Counts

4 → 643

Calls

4 calls:

16.0ms	(/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
37.0ms	(/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
14.0ms	(pow PI (- 1/2 (/ k 2)))
13.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

series932.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
482.0ms	(/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
51.0ms	(pow PI (- 1/2 (/ k 2)))
138.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

simplify3.6s

Counts

655 → 655

Iterations

Iter	Nodes
done	5000
1	2492
0	885

prune2.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (sqrt PI)))
0.3b	(/ (sqrt k) (sqrt PI))
0.8b	(pow n (- 1/2 (/ k 2)))
1.0b	(sqrt PI)

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

757×	`times-frac`
405×	`sqrt-prod`
373×	`add-sqr-sqrt`
369×	`*-un-lft-identity`
367×	`add-cube-cbrt`
126×	`unpow-prod-down`
84×	`unpow-prod-up`
46×	`associate-/r*`
42×	`sub-neg` `sqr-pow`
20×	`add-exp-log`
15×	`associate-/l*`
12×	`div-inv`
11×	`add-cbrt-cube`
10×	`div-exp`
6×	`pow1` `pow-unpow`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-exp`
2×	`clear-num` `frac-2neg` `pow-sub` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-undiv` `pow-pow` `sqrt-pow1` `pow1/2` `associate-/r/` `distribute-lft-out--` `associate-/l/`

Counts

4 → 530

Calls

4 calls:

33.0ms	(/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (sqrt PI)))
11.0ms	(/ (sqrt k) (sqrt PI))
16.0ms	(pow n (- 1/2 (/ k 2)))
2.0ms	(sqrt PI)

series410.0ms

Counts

4 → 10

Calls

4 calls:

190.0ms	(/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (sqrt PI)))
133.0ms	(/ (sqrt k) (sqrt PI))
87.0ms	(pow n (- 1/2 (/ k 2)))
0.0ms	(sqrt PI)

simplify2.2s

Counts

540 → 540

Iterations

Iter	Nodes
done	5000
1	1814
0	669

prune2.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes109.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	14

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.9s	20923×	body	80	nan
2.3s	11902×	body	80	valid