Details

sample176.0ms

Algorithm

intervals

Results

93.0ms	656×	body	80	nan
40.0ms	358×	body	80	valid

simplify945.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1541
4	328
3	120
2	59
1	29
0	13

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* PI (* n 2.0))
1.5b	(pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
25×	`associate-l`
23×	`sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
6×	`associate-/r` `div-exp` `associate-r*` `pow-prod-down` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 149

Calls

4 calls:

34.0ms	(* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
15.0ms	(/ 1.0 (sqrt k))
15.0ms	(* PI (* n 2.0))
15.0ms	(pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))

series728.0ms

Counts

4 → 12

Calls

4 calls:

440.0ms	(* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
57.0ms	(/ 1.0 (sqrt k))
35.0ms	(* PI (* n 2.0))
197.0ms	(pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))

simplify1.7s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	4321
1	979
0	354

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow PI (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow PI (/ (- 1.0 k) 2.0))
1.2b	(pow (* n 2.0) (/ (- 1.0 k) 2.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
72×	`times-frac`
65×	`*-un-lft-identity`
53×	`add-cube-cbrt`
38×	`pow-unpow`
24×	`sqrt-prod`
23×	`add-exp-log`
22×	`associate-l`
11×	`add-cbrt-cube`
10×	`unpow-prod-down`
9×	`unswap-sqr`
8×	`pow1`
7×	`associate-r` `prod-exp`
6×	`associate-/r*` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
5×	`pow-exp`
4×	`pow-to-exp` `div-sub` `div-exp` `div-inv` `pow-sub` `add-log-exp`
3×	`pow-pow` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 164

Calls

4 calls:

41.0ms	(* (/ 1.0 (sqrt k)) (pow PI (/ (- 1.0 k) 2.0)))
5.0ms	(/ 1.0 (sqrt k))
6.0ms	(pow PI (/ (- 1.0 k) 2.0))
9.0ms	(pow (* n 2.0) (/ (- 1.0 k) 2.0))

series587.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(* (/ 1.0 (sqrt k)) (pow PI (/ (- 1.0 k) 2.0)))
72.0ms	(/ 1.0 (sqrt k))
55.0ms	(pow PI (/ (- 1.0 k) 2.0))
159.0ms	(pow (* n 2.0) (/ (- 1.0 k) 2.0))

simplify1.9s

Counts

176 → 176

Iterations

Iter	Nodes
done	5000
2	4022
1	942
0	337

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt (pow PI (/ (- 1.0 k) 2.0))) 1.0) (sqrt k))
0.5b	(pow PI (/ (- 1.0 k) 2.0))
0.5b	(pow PI (/ (- 1.0 k) 2.0))
1.2b	(pow (* n 2.0) (/ (- 1.0 k) 2.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

57×	`pow-unpow`
55×	`add-sqr-sqrt` `*-un-lft-identity`
51×	`times-frac`
37×	`add-cube-cbrt`
14×	`add-exp-log`
9×	`pow1` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
7×	`unpow-prod-down`
6×	`associate-/r*` `sqrt-prod`
4×	`pow-pow` `div-sub` `pow-exp` `div-inv` `pow-sub` `add-log-exp`
3×	`pow-to-exp` `sqr-pow`
2×	`cbrt-undiv` `div-exp` `prod-exp`
1×	`clear-num` `frac-2neg` `sqrt-div` `pow-prod-down` `associate-l/` `cbrt-unprod` `associate-/l` `associate-/l/`

Counts

4 → 130

Calls

4 calls:

24.0ms	(/ (* (sqrt (pow PI (/ (- 1.0 k) 2.0))) 1.0) (sqrt k))
11.0ms	(pow PI (/ (- 1.0 k) 2.0))
12.0ms	(pow PI (/ (- 1.0 k) 2.0))
16.0ms	(pow (* n 2.0) (/ (- 1.0 k) 2.0))

series556.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(/ (* (sqrt (pow PI (/ (- 1.0 k) 2.0))) 1.0) (sqrt k))
69.0ms	(pow PI (/ (- 1.0 k) 2.0))
72.0ms	(pow PI (/ (- 1.0 k) 2.0))
142.0ms	(pow (* n 2.0) (/ (- 1.0 k) 2.0))

simplify1.5s

Counts

142 → 142

Iterations

Iter	Nodes
done	5002
2	3354
1	799
0	277

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt 1.0) (pow PI (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
0.2b	(/ (sqrt 1.0) (sqrt (sqrt k)))
0.5b	(pow PI (/ (- 1.0 k) 2.0))
1.2b	(pow (* n 2.0) (/ (- 1.0 k) 2.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

111×	`sqrt-prod`
93×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
70×	`add-cube-cbrt`
38×	`pow-unpow`
20×	`add-exp-log`
18×	`associate-/r*`
11×	`add-cbrt-cube`
8×	`pow1`
7×	`associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`div-exp`
4×	`unpow-prod-down` `pow-exp` `prod-exp` `div-inv` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-pow` `div-sub` `pow-sub`
2×	`clear-num` `frac-2neg` `sqr-pow`
1×	`sqrt-undiv` `pow-prod-down` `associate-*r/` `cbrt-unprod` `associate-/l/`

Counts

4 → 186

Calls

4 calls:

13.0ms	(/ (* (sqrt 1.0) (pow PI (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
8.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
6.0ms	(pow PI (/ (- 1.0 k) 2.0))
14.0ms	(pow (* n 2.0) (/ (- 1.0 k) 2.0))

series816.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ (* (sqrt 1.0) (pow PI (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
319.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
66.0ms	(pow PI (/ (- 1.0 k) 2.0))
132.0ms	(pow (* n 2.0) (/ (- 1.0 k) 2.0))

simplify1.8s

Counts

198 → 198

Iterations

Iter	Nodes
done	5000
2	4156
1	945
0	364

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes299.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.0s	20122×	body	80	nan
1.6s	11872×	body	80	valid