Details

sample87.0ms

Algorithm

intervals

Results

33.0ms	615×	body	80	nan
23.0ms	389×	body	80	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1044	8
5	5001	8
done	5001	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

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

rewrite88.0ms

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×	`div-exp` `pow-prod-down` `associate-/r*` `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` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 157

Calls

4 calls:

36.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(/ 1.0 (sqrt k))
19.0ms	(* (* 2.0 PI) n)
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series533.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
42.0ms	(/ 1.0 (sqrt k))
32.0ms	(* (* 2.0 PI) n)
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify97.0ms

Counts

169 → 169

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5003	1383
done	5003	1383

prune452.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
136×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
100×	`add-cube-cbrt`
26×	`pow1` `add-exp-log`
18×	`distribute-lft-out--` `difference-of-squares`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
8×	`div-inv`
6×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 200

Calls

4 calls:

16.0ms	(* (* 2.0 PI) n)
16.0ms	(* (* 2.0 PI) n)
27.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
25.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series348.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) n)
38.0ms	(* (* 2.0 PI) n)
136.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
142.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify71.0ms

Counts

212 → 212

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	703	1718
1	2797	1652
2	5001	1636
done	5001	1636

prune688.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite88.0ms

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×	`pow-pow` `pow-exp` `associate-/r*`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod` `associate-/l*`
2×	`pow-to-exp` `unpow-prod-down` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative`

Counts

4 → 221

Calls

4 calls:

18.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
24.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
28.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series356.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 2.0 PI) n)
36.0ms	(/ 1.0 (sqrt k))
143.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
138.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify83.0ms

Counts

233 → 233

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	874	1888
1	3432	1810
2	5001	1792
done	5001	1792

prune747.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt k))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

1098×	`times-frac`
598×	`add-sqr-sqrt` `*-un-lft-identity`
472×	`add-cube-cbrt`
435×	`pow-unpow`
63×	`distribute-lft-out--` `difference-of-squares`
31×	`div-inv`
24×	`add-exp-log`
22×	`pow1`
12×	`sqrt-prod`
9×	`pow-pow` `pow-prod-down` `pow-exp` `prod-exp`
8×	`div-sub`
6×	`associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `unpow-prod-down` `associate-/l*` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`

Counts

4 → 533

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt k))
40.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
40.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
24.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series468.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1.0 (sqrt k))
145.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
138.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
148.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify88.0ms

Counts

545 → 545

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1959	5547
1	5001	5350
done	5001	5350

prune2.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes113.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	25
1	23	25
done	23	25

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.0s	20588×	body	80	nan
739.0ms	12004×	body	80	valid