Details

sample96.0ms

Algorithm

intervals

Results

41.0ms	789×	body	80	nan
22.0ms	385×	body	80	valid

simplify38.0ms

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

rewrite94.0ms

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:

41.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
17.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))
22.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series524.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
32.0ms	(* (* 2.0 PI) n)
40.0ms	(/ 1.0 (sqrt k))
137.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify99.0ms

Counts

161 → 161

Iterations

Useful iterations: 2 (86.0ms)

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

prune428.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))
0.5b	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite95.0ms

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` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-to-exp` `unpow-prod-down` `pow-plus` `sqrt-unprod` `div-sub` `associate-r/` `associate-l/` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `pow-sub` `sqr-pow`

Counts

4 → 241

Calls

4 calls:

8.0ms	(/ 1.0 (sqrt k))
6.0ms	(/ 1.0 (sqrt k))
45.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
23.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series305.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (sqrt k))
40.0ms	(/ 1.0 (sqrt k))
92.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
136.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify98.0ms

Counts

253 → 253

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	747	1810
1	3412	1649
2	5002	1634
done	5002	1634

prune682.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (* 1.0 1.0) k))
0.2b	(* (sqrt (/ (* 1.0 1.0) k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
27×	`add-exp-log`
26×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-cube-cbrt`
19×	`pow-unpow`
18×	`sqrt-prod`
16×	`pow1`
14×	`prod-exp`
11×	`associate-l` `add-cbrt-cube`
8×	`associate-r`
6×	`pow-prod-down` `pow-exp` `unswap-sqr`
5×	`sqr-pow`
4×	`cbrt-unprod` `add-log-exp`
3×	`pow-pow` `sqrt-div` `div-sub` `div-inv` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `*-commutative`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`

Counts

4 → 111

Calls

4 calls:

4.0ms	(sqrt (/ (* 1.0 1.0) k))
42.0ms	(* (sqrt (/ (* 1.0 1.0) k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
17.0ms	(* (* 2.0 PI) n)
23.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series597.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (/ (* 1.0 1.0) k))
373.0ms	(* (sqrt (/ (* 1.0 1.0) k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
35.0ms	(* (* 2.0 PI) n)
135.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify91.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	881	1210
1	3616	1129
2	5002	1124
done	5002	1124

prune363.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (/ (* 1.0 1.0) k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
0.3b	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
0.8b	(pow n (/ (- 1.0 k) 2.0))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
48×	`add-sqr-sqrt`
44×	`prod-exp`
41×	`*-un-lft-identity`
38×	`pow-unpow`
33×	`times-frac`
29×	`add-cube-cbrt`
23×	`pow-exp`
16×	`pow-to-exp`
15×	`associate-l`
14×	`div-sub` `pow-sub`
11×	`add-cbrt-cube`
10×	`pow1` `unpow-prod-down`
9×	`sqr-pow`
8×	`associate-r`
7×	`sqrt-prod`
6×	`frac-times` `associate-*r/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
4×	`sqrt-div` `associate-*l/` `cbrt-unprod` `add-log-exp`
3×	`pow-pow` `pow-prod-down` `div-inv`
2×	`*-commutative`

Counts

4 → 153

Calls

4 calls:

68.0ms	(* (sqrt (/ (* 1.0 1.0) k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
23.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
11.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
8.0ms	(pow n (/ (- 1.0 k) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

650.0ms	(* (sqrt (/ (* 1.0 1.0) k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
275.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
74.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
61.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify106.0ms

Counts

165 → 165

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	1003	1804
1	4048	1682
2	5001	1673
done	5001	1673

prune492.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes214.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	15
1	19	15
done	19	15

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	20965×	body	80	nan
714.0ms	11987×	body	80	valid
0.0ms	1×	body	160	nan