Details

sample228.0ms

Algorithm

intervals

Results

126.0ms	650×	body	80	nan
68.0ms	367×	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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
0.2b	(* n (* 2 PI))
1.3b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

rewrite50.0ms

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))
13.0ms	(* n (* 2 PI))
14.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series505.0ms

Counts

3 → 9

Calls

3 calls:

310.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
58.0ms	(* n (* 2 PI))
138.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

simplify1.5s

Counts

133 → 133

Iterations

Iter	Nodes
2	2339
1	750
0	293

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* n (* 2 PI))
0.2b	(* n (* 2 PI))
1.2b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
1.2b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
166×	`add-sqr-sqrt` `*-un-lft-identity`
140×	`pow-unpow`
112×	`add-cube-cbrt`
36×	`difference-of-squares`
26×	`pow1` `add-exp-log`
18×	`distribute-lft-out--`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
8×	`div-inv`
6×	`pow-pow` `associate-l` `pow-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `div-sub` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-r` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 222

Calls

4 calls:

26.0ms	(* n (* 2 PI))
30.0ms	(* n (* 2 PI))
29.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
20.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

series497.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* n (* 2 PI))
66.0ms	(* n (* 2 PI))
185.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
185.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

simplify1.9s

Counts

234 → 234

Iterations

Iter	Nodes
2	2327
1	812
0	261

prune3.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)))
1.1b	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
1.1b	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
1.2b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

1260×	`times-frac`
714×	`add-sqr-sqrt`
710×	`*-un-lft-identity`
521×	`add-cube-cbrt`
498×	`pow-unpow`
126×	`difference-of-squares`
92×	`add-exp-log`
64×	`prod-exp`
63×	`distribute-lft-out--`
39×	`pow-exp`
30×	`div-inv`
22×	`pow1`
20×	`div-sub`
13×	`pow-to-exp`
11×	`sqr-pow`
10×	`pow-prod-down`
9×	`pow-pow`
7×	`unpow-prod-down` `pow-sub`
6×	`add-cbrt-cube`
5×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
1×	`pow2` `frac-times` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 621

Calls

4 calls:

77.0ms	(* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)))
33.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
40.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
32.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

series846.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)))
214.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
166.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
210.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

simplify1.4s

Counts

633 → 633

Iterations

Iter	Nodes
1	2436
0	702

prune11.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)))
1.1b	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
1.1b	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
1.2b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

1260×	`times-frac`
714×	`add-sqr-sqrt`
710×	`*-un-lft-identity`
521×	`add-cube-cbrt`
498×	`pow-unpow`
126×	`difference-of-squares`
92×	`add-exp-log`
64×	`prod-exp`
63×	`distribute-lft-out--`
39×	`pow-exp`
30×	`div-inv`
22×	`pow1`
20×	`div-sub`
13×	`pow-to-exp`
11×	`sqr-pow`
10×	`pow-prod-down`
9×	`pow-pow`
7×	`unpow-prod-down` `pow-sub`
6×	`add-cbrt-cube`
5×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
1×	`pow2` `frac-times` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 621

Calls

4 calls:

70.0ms	(* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)))
17.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
23.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
25.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

series821.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)))
159.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
179.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
231.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

simplify1.5s

Counts

633 → 633

Iterations

Iter	Nodes
1	2436
0	702

prune10.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	21
1	21
0	17

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.9s	20718×	body	80	nan
2.4s	11890×	body	80	valid
2.0ms	7×	body	160	nan