Details

sample85.0ms

Algorithm

intervals

Results

31.0ms	615×	body	80	nan
23.0ms	389×	body	80	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1034	8
5	5001	8
done	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite92.0ms

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:

39.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(/ 1.0 (sqrt k))
17.0ms	(* (* 2.0 PI) n)
24.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series547.0ms

Counts

4 → 12

Calls

4 calls:

333.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
37.0ms	(/ 1.0 (sqrt k))
37.0ms	(* (* 2.0 PI) n)
140.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify97.0ms

Counts

161 → 161

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5002	1344
done	5002	1344

prune425.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite100.0ms

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:

19.0ms	(* (* 2.0 PI) n)
17.0ms	(* (* 2.0 PI) n)
25.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
29.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series365.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* 2.0 PI) n)
33.0ms	(* (* 2.0 PI) n)
149.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
144.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify73.0ms

Counts

204 → 204

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	696	1678
1	2767	1618
2	5001	1608
done	5001	1608

prune681.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite91.0ms

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:

17.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
25.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
29.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series357.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) n)
37.0ms	(/ 1.0 (sqrt k))
145.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
142.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify90.0ms

Counts

225 → 225

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	859	1848
1	3384	1776
2	5001	1766
done	5001	1766

prune737.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt k))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
0.8b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

1098×	`times-frac`
598×	`add-sqr-sqrt` `*-un-lft-identity`
472×	`add-cube-cbrt`
435×	`pow-unpow`
63×	`distribute-lft-out--` `difference-of-squares`
31×	`div-inv`
24×	`add-exp-log`
22×	`pow1`
12×	`sqrt-prod`
9×	`pow-pow` `pow-prod-down` `pow-exp` `prod-exp`
8×	`div-sub`
6×	`associate-/r*` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-to-exp` `unpow-prod-down` `associate-/l*` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`

Counts

4 → 525

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt k))
40.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
38.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
28.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series473.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (sqrt k))
141.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
146.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
143.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify77.0ms

Counts

537 → 537

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1941	5499
1	5002	5298
done	5002	5298

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes118.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	25
1	23	25
done	23	25

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.0s	20588×	body	80	nan
735.0ms	12004×	body	80	valid