Details

sample152.0ms

Algorithm

intervals

Results

58.0ms	674×	body	80	nan
56.0ms	372×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	2693
5	806
4	285
3	114
2	58
1	29
0	13

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

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	(* (* 2.0 PI) n)
0.2b	(/ 1.0 (sqrt k))
1.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite106.0ms

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×	`associate-/r*` `div-exp` `pow-prod-down` `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` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 149

Calls

4 calls:

49.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
21.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series753.0ms

Counts

4 → 12

Calls

4 calls:

403.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
68.0ms	(* (* 2.0 PI) n)
69.0ms	(/ 1.0 (sqrt k))
214.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.8s

Counts

161 → 161

Iterations

Iter	Nodes
done	5003
2	3265
1	975
0	353

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(/ 1.0 (sqrt k))
0.2b	(/ 1.0 (sqrt k))
1.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
24×	`sqrt-prod`
19×	`pow-unpow` `add-exp-log`
15×	`pow1`
13×	`add-cbrt-cube`
12×	`associate-/r*`
6×	`pow-prod-down` `prod-exp` `associate-/l*`
4×	`add-log-exp`
3×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 132

Calls

4 calls:

14.0ms	(* (* 2.0 PI) n)
5.0ms	(/ 1.0 (sqrt k))
5.0ms	(/ 1.0 (sqrt k))
34.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series361.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* 2.0 PI) n)
51.0ms	(/ 1.0 (sqrt k))
42.0ms	(/ 1.0 (sqrt k))
230.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.8s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1810
1	601
0	236

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
0.3b	(/ 1.0 (sqrt (sqrt k)))
1.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

609×	`times-frac`
606×	`sqrt-prod`
342×	`add-sqr-sqrt` `*-un-lft-identity`
336×	`add-cube-cbrt`
37×	`associate-/l*`
24×	`associate-/r*`
19×	`pow-unpow` `add-exp-log`
14×	`div-inv`
13×	`add-cbrt-cube`
10×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `pow-exp` `prod-exp` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `pow-sub` `sqr-pow` `associate-/l/`

Counts

4 → 460

Calls

4 calls:

5.0ms	(/ 1.0 (sqrt k))
26.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
10.0ms	(/ 1.0 (sqrt (sqrt k)))
17.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series563.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ 1.0 (sqrt k))
45.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
251.0ms	(/ 1.0 (sqrt (sqrt k)))
206.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

472 → 472

Iterations

Iter	Nodes
done	5084
2	3261
1	1370
0	569

prune2.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.2b	(/ 1.0 (sqrt k))
0.4b	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
1.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

200×	`sqrt-prod`
173×	`add-sqr-sqrt`
151×	`times-frac`
109×	`*-un-lft-identity`
103×	`add-cube-cbrt`
33×	`swap-sqr`
25×	`pow1` `associate-r` `associate-l`
19×	`pow-unpow`
16×	`add-exp-log` `unswap-sqr`
12×	`associate-/r*`
10×	`add-cbrt-cube`
8×	`sqrt-pow1` `pow1/2`
7×	`div-inv`
6×	`pow-prod-down` `associate-/l*`
5×	`pow-prod-up`
4×	`sqrt-div` `prod-exp` `add-log-exp`
3×	`pow-pow` `pow-exp` `pow-sqr` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `pow-to-exp` `rem-square-sqrt` `unpow-prod-down` `pow-plus` `sqrt-unprod` `div-sub` `associate-l/` `associate-r/` `*-commutative` `cbrt-unprod` `pow-sub` `sqr-pow`

Counts

4 → 241

Calls

4 calls:

10.0ms	(/ 1.0 (sqrt k))
10.0ms	(/ 1.0 (sqrt k))
52.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
43.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series422.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ 1.0 (sqrt k))
52.0ms	(/ 1.0 (sqrt k))
113.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
197.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.1s

Counts

253 → 253

Iterations

Iter	Nodes
done	5003
2	2196
1	815
0	362

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes603.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.2s	20706×	body	80	nan
1.8s	11897×	body	80	valid
0.0ms	2×	body	160	nan