Details

sample85.0ms

Algorithm

intervals

Results

30.0ms	631×	body	80	nan
25.0ms	382×	body	80	valid

simplify2.3s

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	853	16
6	3196	16
done	5001	16

prune3.0ms

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)))
0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
1.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite91.0ms

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:

38.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
19.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series522.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
35.0ms	(* (* 2.0 PI) n)
37.0ms	(/ 1.0 (sqrt k))
137.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.5s

Counts

169 → 169

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	369	2880
1	961	2712
2	3131	2550
done	5000	2540

prune449.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
1.1b	(pow n (/ (- 1.0 k) 2.0))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
48×	`times-frac`
41×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
16×	`prod-exp`
13×	`pow-exp`
12×	`sqrt-prod`
10×	`unpow-prod-down`
9×	`pow-to-exp` `sqr-pow`
8×	`pow1` `add-cbrt-cube`
7×	`associate-r`
6×	`div-sub` `associate-/r*` `distribute-lft-out--` `pow-sub` `difference-of-squares` `unswap-sqr`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-inv` `associate-/l*`
2×	`pow-prod-down`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `associate-r/` `div-exp` `associate-l/` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

23.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
6.0ms	(/ 1.0 (sqrt k))
11.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
8.0ms	(pow n (/ (- 1.0 k) 2.0))

series461.0ms

Counts

4 → 12

Calls

4 calls:

285.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
37.0ms	(/ 1.0 (sqrt k))
77.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
61.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify1.0s

Counts

170 → 170

Iterations

Useful iterations: done (997.0ms)

Iter	Nodes	Cost
0	324	2568
1	775	2337
2	2301	2238
done	5000	2222

prune517.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt (sqrt k)))
0.3b	(/ 1 (sqrt (sqrt k)))
0.5b	(* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))))
1.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

190×	`add-sqr-sqrt`
171×	`sqrt-prod`
168×	`times-frac`
113×	`*-un-lft-identity`
95×	`add-cube-cbrt`
38×	`add-exp-log`
31×	`associate-r` `associate-l`
28×	`unswap-sqr`
20×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`associate-/r*`
15×	`pow1`
11×	`div-exp` `prod-exp`
6×	`cbrt-undiv` `associate-/l*`
5×	`pow-flip` `div-inv`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `pow-pow` `1-exp` `pow-exp` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `pow1/2` `clear-num`
1×	`frac-times` `pow-to-exp` `unpow-prod-down` `div-sub` `associate-r/` `associate-l/` `*-commutative` `inv-pow` `pow-sub` `sqr-pow`

Counts

4 → 268

Calls

4 calls:

8.0ms	(/ 1.0 (sqrt (sqrt k)))
11.0ms	(/ 1 (sqrt (sqrt k)))
60.0ms	(* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))))
22.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series502.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ 1.0 (sqrt (sqrt k)))
149.0ms	(/ 1 (sqrt (sqrt k)))
44.0ms	(* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))))
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.2s

Counts

280 → 280

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	382	4064
1	961	3506
2	2634	3036
done	5000	3031

prune606.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))))
0.6b	(cbrt k)
0.6b	(cbrt k)
1.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

469×	`add-sqr-sqrt`
446×	`times-frac`
415×	`sqrt-prod`
128×	`*-un-lft-identity`
122×	`add-cube-cbrt`
120×	`cbrt-prod`
94×	`associate-l`
90×	`unswap-sqr`
76×	`associate-r`
42×	`add-exp-log`
28×	`add-cbrt-cube`
19×	`pow-unpow`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp`
12×	`pow1` `div-inv`
10×	`cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `pow-exp` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`frac-times` `pow-to-exp` `unpow-prod-down` `div-sub` `associate-r/` `associate-l/` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 354

Calls

4 calls:

178.0ms	(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))))
1.0ms	(cbrt k)
1.0ms	(cbrt k)
30.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series791.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))))
183.0ms	(cbrt k)
179.0ms	(cbrt k)
140.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.7s

Counts

366 → 366

Iterations

Useful iterations: 2 (799.0ms)

Iter	Nodes	Cost
0	530	10247
1	1530	9876
2	4915	9376
done	5000	9376

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes129.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	23
1	23	23
done	23	23

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.0s	20389×	body	80	nan
722.0ms	11892×	body	80	valid