Details

sample189.0ms

Algorithm

intervals

Results

88.0ms	641×	body	80	nan
70.0ms	381×	body	80	valid

simplify9.2s

Counts

1 → 1

Iterations

Iter	Nodes
7	6317
6	1981
5	831
4	330
3	124
2	62
1	31
0	13

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
0.3b	(* n (* 2 PI))
1.1b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`add-cube-cbrt`
26×	`add-exp-log`
22×	`pow-unpow`
18×	`sqrt-prod`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`unpow-prod-down` `sqr-pow`
6×	`associate-/r*` `pow-prod-down` `pow-exp` `difference-of-squares`
5×	`div-exp` `associate-/l*`
3×	`expm1-log1p-u` `pow-pow` `associate-l` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
2×	`pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `associate-/l/`

Counts

3 → 124

Calls

3 calls:

22.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
30.0ms	(* n (* 2 PI))
15.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series570.0ms

Counts

3 → 9

Calls

3 calls:

336.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
55.0ms	(* n (* 2 PI))
178.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

simplify1.5s

Counts

133 → 133

Iterations

Iter	Nodes
2	2339
1	750
0	293

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
0.1b	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
0.3b	(* n (* 2 PI))
1.1b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
147×	`add-sqr-sqrt` `*-un-lft-identity`
138×	`add-cube-cbrt`
78×	`sqrt-prod`
72×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `div-exp` `sqr-pow`
22×	`pow-unpow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
7×	`div-inv`
6×	`rec-exp` `1-exp` `div-sub` `pow-prod-down` `associate-/r/` `pow-sub` `difference-of-squares`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod` `distribute-lft-out--`
2×	`clear-num` `frac-2neg`
1×	`associate-r` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 303

Calls

4 calls:

18.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
9.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
23.0ms	(* n (* 2 PI))
28.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series943.0ms

Counts

4 → 12

Calls

4 calls:

355.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
376.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
35.0ms	(* n (* 2 PI))
177.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

simplify2.4s

Counts

315 → 315

Iterations

Iter	Nodes
2	4261
1	1448
0	535

prune3.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
0.2b	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
0.3b	(* n (* 2 PI))
1.1b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
146×	`add-sqr-sqrt` `*-un-lft-identity`
137×	`add-cube-cbrt`
78×	`sqrt-prod`
72×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `div-exp` `sqr-pow`
22×	`pow-unpow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
8×	`associate-/l*`
7×	`div-inv`
6×	`rec-exp` `1-exp` `pow-prod-down` `difference-of-squares`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod` `distribute-lft-out--`
2×	`clear-num` `frac-2neg` `div-sub` `pow-sub`
1×	`associate-r` `associate-/r/` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 299

Calls

4 calls:

18.0ms	(/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
23.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
32.0ms	(* n (* 2 PI))
19.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series1.0s

Counts

4 → 12

Calls

4 calls:

416.0ms	(/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
320.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
37.0ms	(* n (* 2 PI))
252.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

simplify2.6s

Counts

311 → 311

Iterations

Iter	Nodes
2	4394
1	1520
0	551

prune4.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
0.2b	(/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
0.4b	(pow (* 2 PI) (/ (- 1 k) 2))
1.1b	(pow n (/ (- 1 k) 2))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
108×	`times-frac`
81×	`*-un-lft-identity`
63×	`add-cube-cbrt`
53×	`add-exp-log`
44×	`pow-unpow`
39×	`sqrt-prod`
34×	`associate-r`
27×	`sqr-pow`
25×	`unpow-prod-down`
20×	`prod-exp`
16×	`div-exp` `pow-exp`
15×	`unswap-sqr`
12×	`difference-of-squares`
11×	`pow-to-exp` `add-cbrt-cube`
8×	`pow1`
7×	`associate-l`
6×	`associate-/r*` `distribute-lft-out--`
5×	`div-sub` `associate-/l*` `pow-sub`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-pow`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 227

Calls

4 calls:

27.0ms	(* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
8.0ms	(/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
7.0ms	(pow (* 2 PI) (/ (- 1 k) 2))
5.0ms	(pow n (/ (- 1 k) 2))

series933.0ms

Counts

4 → 12

Calls

4 calls:

498.0ms	(* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
275.0ms	(/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
93.0ms	(pow (* 2 PI) (/ (- 1 k) 2))
67.0ms	(pow n (/ (- 1 k) 2))

simplify2.5s

Counts

239 → 239

Iterations

Iter	Nodes
2	4005
1	1190
0	427

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes146.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	18
1	18
0	14

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.7s	20500×	body	80	nan
2.5s	11813×	body	80	valid
1.0ms	4×	body	160	nan