Details

sample185.0ms

Algorithm

intervals

Results

79.0ms	665×	body	80	nan
54.0ms	398×	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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

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:

25.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
47.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
24.0ms	(* (* 2.0 PI) n)
10.0ms	(/ 1.0 (sqrt k))

series724.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
428.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
61.0ms	(* (* 2.0 PI) n)
60.0ms	(/ 1.0 (sqrt k))

simplify3.3s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	4865
1	1013
0	361

prune978.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
0.3b	(* (* 2.0 PI) n)

rewrite54.0ms

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×	`expm1-log1p-u` `pow-pow` `associate-r` `log1p-expm1-u` `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 → 92

Calls

3 calls:

17.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
20.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
14.0ms	(* (* 2.0 PI) n)

series591.0ms

Counts

3 → 9

Calls

3 calls:

205.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
351.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
35.0ms	(* (* 2.0 PI) n)

simplify3.2s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	3588
1	765
0	268

prune728.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

70×	`sqrt-prod`
42×	`add-sqr-sqrt`
35×	`add-exp-log`
34×	`times-frac`
29×	`pow1`
26×	`*-un-lft-identity` `add-cube-cbrt`
21×	`add-cbrt-cube`
19×	`associate-r`
17×	`swap-sqr`
15×	`associate-l` `prod-exp`
9×	`pow-prod-down`
8×	`sqrt-pow1` `pow1/2` `cbrt-unprod`
6×	`associate-/r*` `div-exp`
5×	`pow-prod-up` `div-inv`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-exp` `pow-sqr` `*-commutative`
2×	`cbrt-undiv` `associate-*r/`
1×	`pow2` `frac-times` `pow-to-exp` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `div-sub` `associate-l/` `associate-/l` `pow-sub` `associate-/l/`

Counts

4 → 151

Calls

4 calls:

22.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
56.0ms	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
21.0ms	(* (* 2.0 PI) n)
14.0ms	(* (* 2.0 PI) n)

series1.1s

Counts

4 → 12

Calls

4 calls:

423.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
582.0ms	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
64.0ms	(* (* 2.0 PI) n)
37.0ms	(* (* 2.0 PI) n)

simplify4.1s

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
2	4819
1	954
0	346

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize85.0ms

Local error

Found 4 expressions with local error:

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

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

357×	`sqrt-prod`
216×	`times-frac`
130×	`associate-r`
117×	`add-sqr-sqrt`
91×	`*-un-lft-identity` `add-cube-cbrt`
35×	`add-exp-log`
21×	`add-cbrt-cube`
18×	`pow1`
15×	`associate-l` `prod-exp`
12×	`div-inv`
10×	`unswap-sqr`
9×	`pow-prod-down`
8×	`cbrt-unprod`
6×	`associate-/r*` `div-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`pow-exp` `*-commutative`
2×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`frac-times` `pow-to-exp` `clear-num` `frac-2neg` `sqrt-unprod` `div-sub` `associate-l/` `associate-/l` `pow-sub` `associate-/l/`

Counts

4 → 240

Calls

4 calls:

33.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
164.0ms	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
14.0ms	(* (* 2.0 PI) n)
14.0ms	(* (* 2.0 PI) n)

series1.1s

Counts

4 → 12

Calls

4 calls:

483.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
535.0ms	(* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
59.0ms	(* (* 2.0 PI) n)
40.0ms	(* (* 2.0 PI) n)

simplify2.4s

Counts

252 → 252

Iterations

Iter	Nodes
done	5000
1	1366
0	566

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes284.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	23
1	23
0	19

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.8s	20549×	body	80	nan
1.9s	11990×	body	80	valid
0.0ms	2×	body	160	nan