Details

sample166.0ms

Algorithm

intervals

Results

75.0ms	648×	body	80	nan
40.0ms	387×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	120	16
4	330	16
5	1545	16
done	5000	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

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)
0.3b	(/ 1.0 (sqrt k))
0.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite137.0ms

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×	`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 → 149

Calls

4 calls:

61.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
23.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
36.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series744.0ms

Counts

4 → 12

Calls

4 calls:

417.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
54.0ms	(* (* 2.0 PI) n)
45.0ms	(/ 1.0 (sqrt k))
227.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.7s

Counts

161 → 161

Iterations

Useful iterations: 2 (901.0ms)

Iter	Nodes	Cost
0	361	2800
1	1008	2643
2	4741	2477
done	5000	2477

prune732.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.7b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.7b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite156.0ms

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×	`div-sub` `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 → 213

Calls

4 calls:

36.0ms	(* (* 2.0 PI) n)
12.0ms	(/ 1.0 (sqrt k))
52.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
37.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series511.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* 2.0 PI) n)
45.0ms	(/ 1.0 (sqrt k))
239.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
178.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify2.2s

Counts

225 → 225

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	326	3510
1	964	3242
2	4173	3132
done	5000	3128

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))
0.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
24×	`sqrt-prod`
19×	`add-exp-log` `pow-unpow`
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` `frac-2neg` `div-exp` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 132

Calls

4 calls:

19.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
10.0ms	(/ 1.0 (sqrt k))
33.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series362.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* 2.0 PI) n)
52.0ms	(/ 1.0 (sqrt k))
64.0ms	(/ 1.0 (sqrt k))
204.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.7s

Counts

144 → 144

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	234	1642
1	601	1507
2	2709	1405
done	5001	1401

prune710.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(/ 1.0 (sqrt (sqrt k)))
0.3b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
0.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

594×	`sqrt-prod`
591×	`times-frac`
328×	`add-sqr-sqrt` `*-un-lft-identity`
322×	`add-cube-cbrt`
34×	`associate-/l*`
22×	`add-exp-log`
19×	`pow-unpow`
18×	`associate-/r*`
16×	`add-cbrt-cube`
15×	`pow1`
13×	`div-inv`
6×	`pow-prod-down` `prod-exp`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `associate-/l/` `pow-sub` `sqr-pow`

Counts

4 → 439

Calls

4 calls:

29.0ms	(* (* 2.0 PI) n)
17.0ms	(/ 1.0 (sqrt (sqrt k)))
35.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
22.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series538.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* 2.0 PI) n)
248.0ms	(/ 1.0 (sqrt (sqrt k)))
52.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
192.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify893.0ms

Counts

451 → 451

Iterations

Useful iterations: done (863.0ms)

Iter	Nodes	Cost
0	558	8953
1	1422	7629
done	5000	7131

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes180.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
done	20	32

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.8s	20461×	body	80	nan
2.0s	11878×	body	80	valid
0.0ms	1×	body	160	nan