Details

sample155.0ms

Algorithm

intervals

Results

61.0ms	606×	body	80	nan
44.0ms	372×	body	80	valid

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	119	16
4	313	16
5	853	16
6	3196	16
done	5001	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize40.0ms

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))
1.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite162.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 157

Calls

4 calls:

57.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
13.0ms	(/ 1.0 (sqrt k))
47.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series786.0ms

Counts

4 → 12

Calls

4 calls:

474.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
40.0ms	(* (* 2.0 PI) n)
64.0ms	(/ 1.0 (sqrt k))
208.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

169 → 169

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	369	2880
1	961	2712
2	3131	2550
done	5000	2540

prune710.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
70×	`times-frac`
64×	`*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
23×	`sqrt-prod`
22×	`associate-l`
11×	`prod-exp` `add-cbrt-cube`
8×	`pow1`
7×	`pow-exp`
6×	`associate-/r*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`
5×	`unpow-prod-down` `div-exp` `associate-r`
4×	`expm1-log1p-u` `pow-to-exp` `div-sub` `log1p-expm1-u` `div-inv` `pow-sub` `add-log-exp`
3×	`pow-pow` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 169

Calls

4 calls:

73.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
13.0ms	(/ 1.0 (sqrt k))
24.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
16.0ms	(pow n (/ (- 1.0 k) 2.0))

series589.0ms

Counts

4 → 12

Calls

4 calls:

365.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
54.0ms	(/ 1.0 (sqrt k))
90.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
80.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify1.8s

Counts

181 → 181

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	333	2626
1	831	2468
2	2407	2362
done	5000	2337

prune835.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt` `*-un-lft-identity`
63×	`times-frac`
57×	`pow-unpow`
47×	`add-cube-cbrt`
13×	`add-exp-log`
12×	`sqrt-prod`
11×	`pow1`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r*` `add-cbrt-cube`
5×	`unpow-prod-down` `pow-pow` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-to-exp` `div-sub` `associate-/l*` `pow-sub` `sqr-pow`
2×	`pow-prod-down` `prod-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`

Counts

4 → 149

Calls

4 calls:

12.0ms	(/ 1.0 (sqrt k))
24.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
24.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
32.0ms	(pow n (/ (- 1.0 k) 2.0))

series428.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1.0 (sqrt k))
107.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
131.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
128.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify3.5s

Counts

161 → 161

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	246	1851
1	565	1716
2	1464	1668
3	4938	1627
done	5000	1627

prune993.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))
1.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
1.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
64×	`add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow`
24×	`sqrt-prod`
20×	`add-exp-log`
16×	`pow1`
12×	`associate-/r*`
8×	`add-cbrt-cube`
6×	`pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `unpow-prod-down` `frac-2neg` `div-sub` `div-exp` `clear-num` `pow-sub` `sqr-pow`

Counts

4 → 158

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt k))
15.0ms	(/ 1.0 (sqrt k))
42.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
43.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series538.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ 1.0 (sqrt k))
43.0ms	(/ 1.0 (sqrt k))
220.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
198.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.2s

Counts

170 → 170

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	212	2208
1	494	2028
2	1361	1920
done	5000	1880

prune871.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes338.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	34
1	20	34
done	20	34

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.7s	21106×	body	80	nan
2.2s	11995×	body	80	valid
0.0ms	1×	body	160	nan