Details

sample147.0ms

Algorithm

intervals

Results

62.0ms	789×	body	80	nan
34.0ms	385×	body	80	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	119	16
4	313	16
5	843	16
6	3221	16
done	5001	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

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

rewrite102.0ms

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:

41.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
18.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
26.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series773.0ms

Counts

4 → 12

Calls

4 calls:

441.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
58.0ms	(* (* 2.0 PI) n)
48.0ms	(/ 1.0 (sqrt k))
225.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.1s

Counts

161 → 161

Iterations

Useful iterations: 2 (772.0ms)

Iter	Nodes	Cost
0	361	2800
1	931	2635
2	3051	2471
done	5001	2471

prune687.0ms

Pruning

12 alts after pruning (12 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 (sqrt k)))
0.4b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite135.0ms

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:

27.0ms	(* (* 2.0 PI) n)
15.0ms	(/ 1.0 (sqrt (sqrt k)))
27.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
22.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series597.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* 2.0 PI) n)
258.0ms	(/ 1.0 (sqrt (sqrt k)))
63.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
219.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

451 → 451

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	558	8953
1	1320	7629
2	3045	7052
done	5001	6884

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

200×	`sqrt-prod`
173×	`add-sqr-sqrt`
151×	`times-frac`
109×	`*-un-lft-identity`
103×	`add-cube-cbrt`
33×	`swap-sqr`
25×	`pow1` `associate-r` `associate-l`
19×	`pow-unpow`
16×	`add-exp-log` `unswap-sqr`
12×	`associate-/r*`
10×	`add-cbrt-cube`
8×	`sqrt-pow1` `pow1/2`
7×	`div-inv`
6×	`pow-prod-down` `associate-/l*`
5×	`pow-prod-up`
4×	`sqrt-div` `prod-exp` `add-log-exp`
3×	`pow-pow` `pow-exp` `pow-sqr` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-to-exp` `unpow-prod-down` `pow-plus` `sqrt-unprod` `div-sub` `associate-r/` `associate-l/` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `pow-sub` `sqr-pow`

Counts

4 → 241

Calls

4 calls:

12.0ms	(/ 1.0 (sqrt k))
12.0ms	(/ 1.0 (sqrt k))
68.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
37.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series437.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (sqrt k))
52.0ms	(/ 1.0 (sqrt k))
145.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
200.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.5s

Counts

253 → 253

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	360	3916
1	728	2818
2	2126	2679
done	5000	2638

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `sqrt-prod`
35×	`times-frac`
30×	`add-cube-cbrt`
25×	`associate-r`
19×	`pow-unpow`
17×	`pow1`
12×	`add-exp-log`
10×	`sqrt-div`
8×	`pow-prod-down`
6×	`cbrt-prod` `add-cbrt-cube`
5×	`frac-times` `associate-*l/`
4×	`sqrt-pow1` `associate-l` `prod-exp` `add-log-exp` `unswap-sqr`
3×	`pow-pow` `associate-*r/` `pow-exp` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/2` `pow1/3` `div-inv`
1×	`pow-to-exp` `unpow-prod-down` `sqrt-unprod` `div-sub` `*-commutative` `cbrt-unprod` `pow-sub` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

125.0ms	(* (sqrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (sqrt (/ 1.0 (sqrt k))))
1.0ms	(cbrt k)
1.0ms	(cbrt k)
26.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

421.0ms	(* (sqrt (* (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))))) (sqrt (/ 1.0 (sqrt k))))
264.0ms	(cbrt k)
273.0ms	(cbrt k)
236.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.4s

Counts

125 → 125

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	307	2304
1	690	1888
2	2036	1794
done	5000	1742

prune885.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes332.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	32
1	28	32
done	28	32

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	20965×	body	80	nan
1.1s	11987×	body	80	valid
0.0ms	1×	body	160	nan