Details

sample172.0ms

Algorithm

intervals

Results

68.0ms	630×	body	80	nan
49.0ms	385×	body	80	valid

simplify2.2s

Counts: 1 → 1

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(/ 1.0 (sqrt k))
0.2b	(* (* 2.0 PI) n)
1.0b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
8×	`associate-r`
6×	`div-exp` `pow-prod-down` `associate-/r*` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 149

Calls

4 calls:

54.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(/ 1.0 (sqrt k))
18.0ms	(* (* 2.0 PI) n)
29.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series787.0ms

Counts

4 → 12

Calls

4 calls:

484.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
56.0ms	(/ 1.0 (sqrt k))
39.0ms	(* (* 2.0 PI) n)
207.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.9s

Counts: 161 → 161

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
0.2b	(* (* 2.0 PI) n)
1.0b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
38×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`add-cube-cbrt`
26×	`add-exp-log`
19×	`pow-unpow`
18×	`sqrt-prod`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`unpow-prod-down` `sqr-pow`
6×	`pow-prod-down` `pow-exp` `associate-/r*`
5×	`div-exp` `associate-/l*`
3×	`pow-pow` `associate-r` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`cbrt-undiv` `frac-2neg` `associate-l` `clear-num` `*-commutative` `associate-/l/`

Counts

3 → 112

Calls

3 calls:

27.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
36.0ms	(* (* 2.0 PI) n)
51.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series627.0ms

Counts

3 → 9

Calls

3 calls:

347.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
42.0ms	(* (* 2.0 PI) n)
238.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.3s

Counts: 121 → 121

prune601.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(/ 1.0 (sqrt k))
0.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
150×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
114×	`add-cube-cbrt`
23×	`add-exp-log`
21×	`pow1`
18×	`distribute-lft-out--` `difference-of-squares`
12×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `div-inv`
6×	`pow-pow` `pow-exp` `associate-/r*`
4×	`div-sub` `add-log-exp`
3×	`associate-r` `cbrt-unprod` `associate-/l*`
2×	`pow-to-exp` `unpow-prod-down` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative`

Counts

4 → 213

Calls

4 calls:

32.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
39.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
66.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series510.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* 2.0 PI) n)
58.0ms	(/ 1.0 (sqrt k))
194.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
194.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify1.5s

Counts: 225 → 225

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 192

Calls

4 calls:

18.0ms	(* (* 2.0 PI) n)
19.0ms	(* (* 2.0 PI) n)
58.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
54.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series542.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (* 2.0 PI) n)
64.0ms	(* (* 2.0 PI) n)
227.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
207.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify1.2s

Counts: 204 → 204

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes158.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.9s

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.4s	20065×	body	80	nan
1.7s	11893×	body	80	valid