Details

sample251.0ms

Algorithm

intervals

Results

114.0ms	625×	body	80	nan
105.0ms	383×	body	80	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	2083
5	817
4	322
3	123
2	60
1	29
0	13

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

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

rewrite75.0ms

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` `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 → 115

Calls

3 calls:

20.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
22.0ms	(* n (* 2 PI))
30.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series597.0ms

Counts

3 → 9

Calls

3 calls:

333.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
40.0ms	(* n (* 2 PI))
224.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.3s

Counts

124 → 124

Iterations

Iter	Nodes
2	2006
1	640
0	264

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.3b	(* (* 2 PI) n)
0.3b	(/ 1 (sqrt k))
0.4b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt` `add-exp-log`
62×	`times-frac`
57×	`*-un-lft-identity`
44×	`add-cube-cbrt`
38×	`prod-exp`
25×	`sqrt-prod`
23×	`associate-l`
22×	`pow-unpow`
17×	`pow1`
16×	`add-cbrt-cube`
15×	`pow-exp`
12×	`div-exp`
10×	`unswap-sqr`
8×	`associate-r`
7×	`sqr-pow`
6×	`rec-exp` `associate-/r*` `1-exp` `pow-prod-down` `difference-of-squares`
5×	`pow-to-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-pow` `div-sub` `div-inv` `pow-flip` `associate-/l*` `distribute-lft-out--` `pow-sub`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `inv-pow`

Counts

4 → 172

Calls

4 calls:

56.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
24.0ms	(* (* 2 PI) n)
8.0ms	(/ 1 (sqrt k))
27.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series644.0ms

Counts

4 → 12

Calls

4 calls:

357.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
53.0ms	(* (* 2 PI) n)
47.0ms	(/ 1 (sqrt k))
187.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.8s

Counts

184 → 184

Iterations

Iter	Nodes
2	2733
1	916
0	341

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.3b	(* (* 2 PI) n)
0.4b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
33×	`add-sqr-sqrt`
30×	`prod-exp`
26×	`*-un-lft-identity`
22×	`pow-unpow`
18×	`times-frac`
17×	`pow-exp` `add-cube-cbrt`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`pow-to-exp`
8×	`associate-r` `associate-l` `sqr-pow`
7×	`unpow-prod-down`
6×	`pow-prod-down` `difference-of-squares` `unswap-sqr`
4×	`cbrt-unprod`
3×	`pow-pow` `distribute-lft-out--` `add-log-exp`
2×	`div-sub` `*-commutative` `pow-sub`
1×	`associate-*r/` `div-inv`

Counts

3 → 100

Calls

3 calls:

19.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
24.0ms	(* (* 2 PI) n)
17.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series583.0ms

Counts

3 → 9

Calls

3 calls:

322.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
54.0ms	(* (* 2 PI) n)
206.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
2	2399
1	709
0	255

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
0.3b	(* (* PI 2) n)
0.4b	(pow (* (* PI 2) n) (/ (- 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×	`pow-pow` `associate-r` `cbrt-unprod` `distribute-lft-out--` `add-log-exp`
2×	`pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-l` `*-commutative` `associate-/l/`

Counts

3 → 115

Calls

3 calls:

9.0ms	(/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
12.0ms	(* (* PI 2) n)
26.0ms	(pow (* (* PI 2) n) (/ (- 1 k) 2))

series611.0ms

Counts

3 → 9

Calls

3 calls:

325.0ms	(/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
58.0ms	(* (* PI 2) n)
229.0ms	(pow (* (* PI 2) n) (/ (- 1 k) 2))

simplify1.6s

Counts

124 → 124

Iterations

Iter	Nodes
2	2309
1	739
0	289

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes190.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	14
1	14
0	12

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.6s	21239×	body	80	nan
2.7s	11990×	body	80	valid
1.0ms	3×	body	160	nan