Details

sample254.0ms

Algorithm

intervals

Results

140.0ms	629×	body	80	nan
79.0ms	398×	body	80	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	2053
5	821
4	322
3	123
2	60
1	29
0	13

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
0.3b	(* PI (* n 2))
0.7b	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

493×	`times-frac`
383×	`add-sqr-sqrt`
380×	`*-un-lft-identity`
378×	`add-cube-cbrt`
328×	`unpow-prod-up`
312×	`prod-diff`
141×	`sqrt-prod`
46×	`associate-/l*`
26×	`add-exp-log`
25×	`div-inv`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sub-neg` `unpow-prod-down` `sqr-pow`
6×	`pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp`
3×	`expm1-log1p-u` `pow-pow` `associate-l` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `distribute-lft-out--` `associate-/l/`

Counts

3 → 436

Calls

3 calls:

17.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
26.0ms	(* PI (* n 2))
17.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

series562.0ms

Counts

3 → 9

Calls

3 calls:

309.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
42.0ms	(* PI (* n 2))
211.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

simplify3.2s

Counts

445 → 445

Iterations

Iter	Nodes
2	4287
1	1515
0	698

prune6.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.3b	(/ 1 (sqrt k))
0.3b	(* (* 2 PI) n)
0.7b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

rewrite108.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 184

Calls

4 calls:

35.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
8.0ms	(/ 1 (sqrt k))
26.0ms	(* (* 2 PI) n)
36.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series738.0ms

Counts

4 → 12

Calls

4 calls:

372.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
49.0ms	(/ 1 (sqrt k))
71.0ms	(* (* 2 PI) n)
245.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.7s

Counts

196 → 196

Iterations

Iter	Nodes
2	2859
1	944
0	353

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
0.3b	(* (* PI 2) n)
0.7b	(pow (* (* PI 2) n) (/ (- 1 k) 2))

rewrite82.0ms

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-r` `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-l` `*-commutative` `associate-/l/`

Counts

3 → 124

Calls

3 calls:

19.0ms	(/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
29.0ms	(* (* PI 2) n)
32.0ms	(pow (* (* PI 2) n) (/ (- 1 k) 2))

series585.0ms

Counts

3 → 9

Calls

3 calls:

335.0ms	(/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
50.0ms	(* (* PI 2) n)
200.0ms	(pow (* (* PI 2) n) (/ (- 1 k) 2))

simplify1.6s

Counts

133 → 133

Iterations

Iter	Nodes
2	2395
1	764
0	298

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

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)
0.7b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

rewrite59.0ms

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×	`expm1-log1p-u` `pow-pow` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
2×	`div-sub` `*-commutative` `pow-sub`
1×	`associate-*r/` `div-inv`

Counts

3 → 109

Calls

3 calls:

25.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
14.0ms	(* (* 2 PI) n)
17.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series640.0ms

Counts

3 → 9

Calls

3 calls:

390.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
60.0ms	(* (* 2 PI) n)
190.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.7s

Counts

118 → 118

Iterations

Iter	Nodes
2	2482
1	731
0	264

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes210.0ms

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	19
1	19
0	15

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.2s	21022×	body	80	nan
2.4s	11987×	body	80	valid
0.0ms	2×	body	160	nan