Details

sample155.0ms

Algorithm

intervals

Results

67.0ms	676×	body	80	nan
36.0ms	342×	body	80	valid

simplify1.1s

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: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(* (* 2.0 PI) n)
0.2b	(/ 1.0 (sqrt k))
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite146.0ms

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:

62.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
26.0ms	(* (* 2.0 PI) n)
9.0ms	(/ 1.0 (sqrt k))
39.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series749.0ms

Counts

4 → 12

Calls

4 calls:

440.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
52.0ms	(* (* 2.0 PI) n)
57.0ms	(/ 1.0 (sqrt k))
200.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.1s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	4715
1	986
0	353

prune922.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
0.2b	(* (* 2.0 PI) n)
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
23×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`times-frac`
19×	`pow-unpow`
17×	`add-cube-cbrt`
14×	`pow1` `prod-exp`
13×	`add-cbrt-cube`
6×	`associate-/r*` `div-exp` `pow-prod-down` `pow-exp` `sqrt-prod`
4×	`cbrt-unprod`
3×	`pow-pow` `associate-r` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`pow-to-exp` `cbrt-undiv` `div-sub` `div-inv` `pow-sub`
1×	`clear-num` `unpow-prod-down` `frac-2neg` `associate-l` `associate-r/` `-commutative` `associate-/l*` `sqr-pow` `associate-/l/`

Counts

3 → 86

Calls

3 calls:

23.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
13.0ms	(* (* 2.0 PI) n)
37.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series663.0ms

Counts

3 → 9

Calls

3 calls:

385.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
63.0ms	(* (* 2.0 PI) n)
216.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.9s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	3459
1	741
0	262

prune684.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (/ (sqrt k) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))))
0.1b	(/ (sqrt k) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)))
0.2b	(* PI n)
1.1b	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
146×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
138×	`add-cube-cbrt`
78×	`sqrt-prod`
43×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `sqr-pow`
19×	`pow-unpow`
16×	`div-exp`
13×	`add-cbrt-cube`
12×	`pow1`
10×	`prod-exp`
9×	`pow-exp` `associate-/l*`
7×	`div-inv`
6×	`div-sub` `associate-/r/` `pow-sub`
4×	`cbrt-undiv` `pow-prod-down` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`clear-num` `frac-2neg`
1×	`*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 274

Calls

4 calls:

41.0ms	(/ 1.0 (/ (sqrt k) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))))
9.0ms	(/ (sqrt k) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)))
5.0ms	(* PI n)
15.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

422.0ms	(/ 1.0 (/ (sqrt k) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))))
598.0ms	(/ (sqrt k) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)))
25.0ms	(* PI n)
224.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

simplify940.0ms

Counts

286 → 286

Iterations

Iter	Nodes
done	5001
1	1669
0	597

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0)))
0.2b	(* PI n)
0.2b	(/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0))))
1.1b	(pow (* PI n) (/ (- 1.0 k) 2.0))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

140×	`times-frac`
83×	`add-exp-log`
76×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
68×	`add-cube-cbrt`
48×	`sqrt-prod`
40×	`associate-/r*` `div-exp`
22×	`prod-exp`
20×	`unpow-prod-down` `add-cbrt-cube` `sqr-pow`
19×	`pow-unpow`
17×	`pow-exp`
11×	`pow-to-exp`
9×	`pow1`
7×	`cbrt-undiv` `associate-/l*`
5×	`div-sub` `div-inv` `pow-sub`
4×	`associate-/r/` `add-log-exp`
3×	`associate-r` `associate-l` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down`
1×	`associate-r/` `-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 216

Calls

4 calls:

8.0ms	(/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0)))
10.0ms	(* PI n)
29.0ms	(/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0))))
13.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

338.0ms	(/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0)))
37.0ms	(* PI n)
888.0ms	(/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0))))
181.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))

simplify737.0ms

Counts

228 → 228

Iterations

Iter	Nodes
done	5000
1	1530
0	525

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes199.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	13

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.8s	20956×	body	80	nan
1.8s	12077×	body	80	valid
1.0ms	3×	body	160	nan