Details

sample161.0ms

Algorithm

intervals

Results

77.0ms	668×	body	80	nan
41.0ms	384×	body	80	valid

simplify5.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	495
1	29	495
2	58	495
3	114	495
4	285	495
5	806	495
6	2693	495
done	5001	495

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
1.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
8×	`associate-r`
6×	`associate-/r*` `div-exp` `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:

54.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
14.0ms	(* (* 2.0 PI) n)
5.0ms	(/ 1.0 (sqrt k))
40.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series782.0ms

Counts

4 → 12

Calls

4 calls:

441.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
62.0ms	(* (* 2.0 PI) n)
71.0ms	(/ 1.0 (sqrt k))
207.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify5.0s

Counts

161 → 161

Iterations

Useful iterations: done (5.0s)

Iter	Nodes	Cost
0	353	73141
1	975	65913
2	3265	65170
done	5003	64970

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
1.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
150×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
114×	`add-cube-cbrt`
23×	`add-exp-log`
21×	`pow1`
18×	`distribute-lft-out--` `difference-of-squares`
12×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `div-inv`
6×	`associate-/r*` `pow-pow` `pow-exp`
4×	`div-sub` `add-log-exp`
3×	`associate-r` `cbrt-unprod` `associate-/l*`
2×	`pow-to-exp` `unpow-prod-down` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-l` `*-commutative`

Counts

4 → 213

Calls

4 calls:

27.0ms	(* (* 2.0 PI) n)
14.0ms	(/ 1.0 (sqrt k))
43.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
29.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series455.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* 2.0 PI) n)
52.0ms	(/ 1.0 (sqrt k))
199.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
151.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify2.9s

Counts

225 → 225

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	328	99765
1	938	91240
2	2615	90178
done	5002	89898

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))
1.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
164×	`add-sqr-sqrt` `*-un-lft-identity`
128×	`add-cube-cbrt`
122×	`pow-unpow`
24×	`sqrt-prod`
20×	`add-exp-log`
18×	`distribute-lft-out--` `difference-of-squares`
16×	`pow1`
12×	`associate-/r*`
10×	`div-inv`
8×	`add-cbrt-cube`
6×	`pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `associate-/l*`
4×	`div-sub` `add-log-exp`
2×	`pow-to-exp` `cbrt-undiv` `clear-num` `unpow-prod-down` `frac-2neg` `div-exp` `pow-sub` `sqr-pow`

Counts

4 → 234

Calls

4 calls:

5.0ms	(/ 1.0 (sqrt k))
5.0ms	(/ 1.0 (sqrt k))
30.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
30.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series542.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1.0 (sqrt k))
72.0ms	(/ 1.0 (sqrt k))
186.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
216.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify3.1s

Counts

246 → 246

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	302	107820
1	856	97786
2	2317	96442
done	5002	96442

prune2.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt 1.0) (sqrt (sqrt k)))
0.3b	(/ (sqrt 1.0) (sqrt (sqrt k)))
0.5b	(* (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))))
1.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

834×	`sqrt-prod`
623×	`add-sqr-sqrt`
555×	`times-frac`
285×	`*-un-lft-identity`
279×	`add-cube-cbrt`
124×	`swap-sqr`
58×	`associate-r` `associate-l`
49×	`unswap-sqr`
26×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`associate-/r*`
17×	`pow1`
12×	`associate-/l*`
7×	`prod-exp` `div-inv`
6×	`cbrt-undiv` `sqrt-undiv` `div-exp`
4×	`pow-prod-down` `cbrt-unprod` `add-log-exp`
3×	`pow-pow` `pow-exp` `distribute-lft-out--` `difference-of-squares`
2×	`clear-num` `frac-2neg`
1×	`pow2` `frac-times` `pow-to-exp` `rem-square-sqrt` `unpow-prod-down` `pow-plus` `sqrt-unprod` `div-sub` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `pow-sub` `sqr-pow`

Counts

4 → 515

Calls

4 calls:

8.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
8.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
120.0ms	(* (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))))
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series954.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
266.0ms	(/ (sqrt 1.0) (sqrt (sqrt k)))
152.0ms	(* (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))))
222.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify3.7s

Counts

527 → 527

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	418	235461
1	1354	216589
2	3956	208551
done	5000	203591

prune2.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes325.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	576
1	20	576
done	20	576

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.4s	20831×	body	80	nan
2.3s	12016×	body	80	valid
0.0ms	1×	body	160	nan