Details

sample120.0ms

Algorithm

intervals

Results

63.0ms	760×	body	80	nan
26.0ms	365×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1551
4	328
3	120
2	59
1	29
0	13

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite132.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 157

Calls

4 calls:

60.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
9.0ms	(/ 1.0 (sqrt k))
26.0ms	(* (* 2.0 PI) n)
25.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series787.0ms

Counts

4 → 12

Calls

4 calls:

470.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
67.0ms	(/ 1.0 (sqrt k))
55.0ms	(* (* 2.0 PI) n)
195.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify4.2s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	4865
1	1013
0	361

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite87.0ms

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-r`
23×	`sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
6×	`associate-/r` `div-exp` `associate-l*` `pow-prod-down` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 157

Calls

4 calls:

34.0ms	(* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
8.0ms	(/ 1.0 (sqrt k))
22.0ms	(* (* 2.0 PI) n)
17.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series806.0ms

Counts

4 → 12

Calls

4 calls:

466.0ms	(* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
58.0ms	(/ 1.0 (sqrt k))
58.0ms	(* (* 2.0 PI) n)
224.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.1s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
1	962
0	343

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.5b	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

188×	`sqrt-prod`
159×	`add-sqr-sqrt`
133×	`times-frac`
95×	`*-un-lft-identity`
89×	`add-cube-cbrt`
33×	`swap-sqr`
30×	`pow1`
28×	`associate-r`
26×	`associate-l`
19×	`pow-unpow` `add-exp-log`
16×	`unswap-sqr`
13×	`add-cbrt-cube`
9×	`pow-prod-down`
8×	`sqrt-pow1` `pow1/2`
7×	`prod-exp`
6×	`associate-/r*` `div-inv`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sqrt-div` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `pow-exp` `pow-sqr` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative`
1×	`pow2` `frac-times` `pow-to-exp` `cbrt-undiv` `clear-num` `rem-square-sqrt` `unpow-prod-down` `frac-2neg` `pow-plus` `sqrt-unprod` `div-sub` `div-exp` `associate-l/` `associate-r/` `pow-sub` `sqr-pow`

Counts

4 → 228

Calls

4 calls:

5.0ms	(/ 1.0 (sqrt k))
14.0ms	(* (* 2.0 PI) n)
59.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
32.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series795.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ 1.0 (sqrt k))
40.0ms	(* (* 2.0 PI) n)
110.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
576.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.4s

Counts

240 → 240

Iterations

Iter	Nodes
done	5000
2	4310
1	931
0	396

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))))
0.6b	(cbrt k)
0.6b	(cbrt k)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

306×	`sqrt-prod`
283×	`times-frac`
255×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
133×	`add-cube-cbrt`
124×	`associate-r`
53×	`cbrt-prod`
32×	`unswap-sqr`
25×	`associate-l`
19×	`pow-unpow`
14×	`pow1`
12×	`add-exp-log` `div-inv`
6×	`add-cbrt-cube` `pow-prod-down`
4×	`expm1-log1p-u` `sqrt-div` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `pow-exp` `distribute-lft-out--` `difference-of-squares`
2×	`sqrt-pow1` `pow1/2` `pow1/3`
1×	`frac-times` `pow-to-exp` `unpow-prod-down` `sqrt-unprod` `div-sub` `associate-l/` `associate-r/` `*-commutative` `cbrt-unprod` `pow-sub` `sqr-pow`

Counts

4 → 264

Calls

4 calls:

134.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))))
1.0ms	(cbrt k)
1.0ms	(cbrt k)
41.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

477.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))))
340.0ms	(cbrt k)
320.0ms	(cbrt k)
207.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify3.2s

Counts

276 → 276

Iterations

Iter	Nodes
done	5000
2	4634
1	1285
0	626

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes234.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.8s	20608×	body	80	nan
1.7s	11771×	body	80	valid