Details

sample208.0ms

Algorithm

intervals

Results

95.0ms	650×	body	80	nan
85.0ms	367×	body	80	valid

simplify8.7s

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite71.0ms

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:

25.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
24.0ms	(* n (* 2 PI))
15.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series892.0ms

Counts

3 → 9

Calls

3 calls:

335.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
356.0ms	(* n (* 2 PI))
201.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.1s

Counts

127 → 127

Iterations

Iter	Nodes
2	2029
1	645
0	267

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
44×	`pow-unpow`
42×	`times-frac`
38×	`*-un-lft-identity`
26×	`pow1` `add-exp-log` `add-cube-cbrt`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `difference-of-squares`
6×	`pow-pow` `associate-l` `pow-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`insert-posit16` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-r` `*-commutative` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

14.0ms	(* n (* 2 PI))
13.0ms	(* n (* 2 PI))
20.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
16.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

series459.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* n (* 2 PI))
48.0ms	(* n (* 2 PI))
216.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
159.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

simplify2.7s

Counts

130 → 130

Iterations

Iter	Nodes
3	4823
2	1358
1	448
0	161

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* n (* 2 PI))
0.2b	(* n (* 2 PI))
1.2b	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
1.3b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
28×	`pow-unpow`
26×	`pow1` `add-exp-log`
25×	`*-un-lft-identity`
22×	`times-frac`
17×	`add-cube-cbrt`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
8×	`difference-of-squares`
6×	`pow-pow` `associate-l` `pow-exp` `cbrt-unprod`
4×	`insert-posit16` `distribute-lft-out--` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-up` `unpow-prod-down` `associate-r` `*-commutative` `pow-sub` `sqr-pow`
1×	`sub-neg` `div-sub` `div-inv`

Counts

4 → 104

Calls

4 calls:

17.0ms	(* n (* 2 PI))
13.0ms	(* n (* 2 PI))
25.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
30.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* n (* 2 PI))
33.0ms	(* n (* 2 PI))
224.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
198.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify4.8s

Counts

116 → 116

Iterations

Iter	Nodes
3	7099
2	1913
1	603
0	206

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1` `add-exp-log`
18×	`add-sqr-sqrt`
14×	`add-cbrt-cube`
12×	`pow-unpow` `*-un-lft-identity` `pow-prod-down` `prod-exp`
8×	`add-cube-cbrt`
6×	`pow-pow` `associate-l` `pow-exp` `cbrt-unprod`
4×	`unpow-prod-up` `insert-posit16` `add-log-exp` `difference-of-squares`
2×	`pow-to-exp` `sub-neg` `unpow-prod-down` `times-frac` `associate-r` `*-commutative` `distribute-lft-out--` `pow-sub` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

21.0ms	(* n (* 2 PI))
14.0ms	(* n (* 2 PI))
20.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
22.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* n (* 2 PI))
45.0ms	(* n (* 2 PI))
155.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
183.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify2.5s

Counts

102 → 102

Iterations

Iter	Nodes
3	3969
2	1098
1	339
0	123

prune1.6s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes159.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	22
1	22
0	18

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.6s	20718×	body	80	nan
2.2s	11890×	body	80	valid
2.0ms	7×	body	160	nan