Details

sample203.0ms

Algorithm

intervals

Results

110.0ms	698×	body	80	nan
63.0ms	385×	body	80	valid

simplify8.8s

Counts

1 → 1

Iterations

Iter	Nodes
7	6334
6	1992
5	827
4	330
3	124
2	62
1	31
0	13

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
0.3b	(* n (* 2 PI))
0.8b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt`
26×	`add-exp-log`
24×	`sqrt-prod`
16×	`unpow-prod-up`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sub-neg` `unpow-prod-down` `sqr-pow`
7×	`associate-/l*`
6×	`pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `div-inv` `distribute-lft-out--` `associate-/l/`

Counts

3 → 118

Calls

3 calls:

23.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
13.0ms	(* n (* 2 PI))
20.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series524.0ms

Counts

3 → 9

Calls

3 calls:

265.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
57.0ms	(* n (* 2 PI))
201.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.2s

Counts

127 → 127

Iterations

Iter	Nodes
2	2029
1	645
0	267

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
0.2b	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
0.3b	(* n (* 2 PI))
0.8b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

352×	`times-frac`
166×	`add-sqr-sqrt`
163×	`*-un-lft-identity`
161×	`add-cube-cbrt`
108×	`sqrt-prod`
72×	`add-exp-log`
64×	`unpow-prod-up`
54×	`associate-/r*`
32×	`sub-neg` `unpow-prod-down` `div-exp` `sqr-pow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
6×	`rec-exp` `pow-unpow` `1-exp` `pow-prod-down` `associate-/r/` `div-inv` `pow-sub`
5×	`pow-to-exp`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`associate-r` `*-commutative` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 343

Calls

4 calls:

27.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
10.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
13.0ms	(* n (* 2 PI))
17.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series837.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
350.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
44.0ms	(* n (* 2 PI))
150.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify2.3s

Counts

355 → 355

Iterations

Iter	Nodes
2	4327
1	1425
0	532

prune4.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (sqrt k))
0.2b	(sqrt (sqrt k))
0.3b	(* n (* 2 PI))
0.8b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

20×	`sqrt-prod`
19×	`add-sqr-sqrt` `pow1`
15×	`add-exp-log`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`add-cbrt-cube`
8×	`sqrt-pow1`
6×	`pow-unpow` `pow-prod-down` `prod-exp`
4×	`rem-sqrt-square` `pow1/2` `insert-posit16` `add-log-exp`
3×	`pow-pow` `associate-l` `pow-exp` `cbrt-unprod`
2×	`unpow-prod-up` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `unpow-prod-down` `times-frac` `associate-r` `*-commutative` `distribute-lft-out--` `pow-sub` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

1.0ms	(sqrt (sqrt k))
1.0ms	(sqrt (sqrt k))
17.0ms	(* n (* 2 PI))
29.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series710.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(sqrt (sqrt k))
191.0ms	(sqrt (sqrt k))
53.0ms	(* n (* 2 PI))
221.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify3.3s

Counts

97 → 97

Iterations

Iter	Nodes
3	4634
2	1320
1	431
0	169

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (sqrt k))
0.3b	(* n (* 2 PI))
0.3b	(/ 1 (sqrt (sqrt k)))
0.8b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

46×	`sqrt-prod`
37×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
30×	`add-cube-cbrt`
28×	`times-frac`
20×	`pow1`
19×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`associate-/r*`
8×	`sqrt-pow1`
6×	`pow-unpow` `pow-prod-down` `prod-exp`
5×	`pow-flip`
4×	`pow1/2` `insert-posit16` `add-log-exp`
3×	`pow-pow` `associate-l` `pow-exp` `cbrt-unprod` `associate-/l*`
2×	`unpow-prod-up` `rem-sqrt-square` `div-exp` `difference-of-squares`
1×	`pow-to-exp` `cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `unpow-prod-down` `frac-2neg` `1-exp` `associate-r` `*-commutative` `div-inv` `distribute-lft-out--` `inv-pow` `pow-sub` `sqr-pow`

Counts

4 → 125

Calls

4 calls:

1.0ms	(sqrt (sqrt k))
12.0ms	(* n (* 2 PI))
6.0ms	(/ 1 (sqrt (sqrt k)))
21.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series668.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(sqrt (sqrt k))
39.0ms	(* n (* 2 PI))
213.0ms	(/ 1 (sqrt (sqrt k)))
209.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify3.4s

Counts

137 → 137

Iterations

Iter	Nodes
3	5143
2	1525
1	535
0	232

prune1.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes146.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
2	21
1	21
0	16

end0.0ms

sample7.1s

Algorithm

intervals

Results

4.2s	19873×	body	80	nan
2.2s	11755×	body	80	valid
1.0ms	2×	body	160	nan