Details

sample115.0ms

Algorithm

intervals

Results

50.0ms	661×	body	80	nan
31.0ms	379×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune9.0ms

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

rewrite113.0ms

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:

37.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
22.0ms	(* (* 2.0 PI) n)
15.0ms	(/ 1.0 (sqrt k))
32.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series756.0ms

Counts

4 → 12

Calls

4 calls:

456.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
46.0ms	(* (* 2.0 PI) n)
46.0ms	(/ 1.0 (sqrt k))
207.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify3.0s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	4715
1	986
0	353

prune897.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

32.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
5.0ms	(/ 1.0 (sqrt k))
16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series386.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (* 2.0 PI) n)
45.0ms	(/ 1.0 (sqrt k))
78.0ms	(/ 1.0 (sqrt k))
192.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.0s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	2695
1	605
0	236

prune954.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize90.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

609×	`times-frac`
606×	`sqrt-prod`
342×	`add-sqr-sqrt` `*-un-lft-identity`
336×	`add-cube-cbrt`
37×	`associate-/l*`
24×	`associate-/r*`
19×	`pow-unpow` `add-exp-log`
14×	`div-inv`
13×	`add-cbrt-cube`
10×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `pow-exp` `prod-exp` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `pow-sub` `sqr-pow` `associate-/l/`

Counts

4 → 460

Calls

4 calls:

5.0ms	(/ 1.0 (sqrt k))
8.0ms	(/ 1.0 (sqrt (sqrt k)))
34.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
31.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series611.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 1.0 (sqrt k))
257.0ms	(/ 1.0 (sqrt (sqrt k)))
52.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
224.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.4s

Counts

472 → 472

Iterations

Iter	Nodes
done	5000
1	1415
0	569

prune2.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.4b	(pow n (/ (- 1.0 k) 2.0))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
70×	`times-frac`
64×	`*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
23×	`sqrt-prod`
22×	`associate-l`
11×	`add-cbrt-cube` `prod-exp`
8×	`pow1`
7×	`pow-exp`
6×	`associate-/r*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`
5×	`unpow-prod-down` `div-exp` `associate-r`
4×	`pow-to-exp` `div-sub` `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 → 161

Calls

4 calls:

5.0ms	(/ 1.0 (sqrt k))
28.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
6.0ms	(pow n (/ (- 1.0 k) 2.0))
9.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ 1.0 (sqrt k))
427.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
77.0ms	(pow n (/ (- 1.0 k) 2.0))
461.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	3733
1	903
0	326

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes301.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	23
1	23
0	19

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.5s	19957×	body	80	nan
1.9s	11812×	body	80	valid
0.0ms	1×	body	160	nan