Details

sample151.0ms

Algorithm

intervals

Results

81.0ms	608×	body	80	nan
38.0ms	355×	body	80	valid

simplify4.2s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize16.0ms

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

rewrite150.0ms

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:

65.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
26.0ms	(* (* 2.0 PI) n)
11.0ms	(/ 1.0 (sqrt k))
40.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series763.0ms

Counts

4 → 12

Calls

4 calls:

421.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
47.0ms	(* (* 2.0 PI) n)
62.0ms	(/ 1.0 (sqrt k))
232.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

169 → 169

Iterations

Useful iterations: done (2.3s)

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

prune700.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.2b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.4b	(pow n (/ (- 1.0 k) 2.0))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite97.0ms

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:

11.0ms	(/ 1.0 (sqrt k))
53.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
8.0ms	(pow n (/ (- 1.0 k) 2.0))
12.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series697.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1.0 (sqrt k))
433.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
86.0ms	(pow n (/ (- 1.0 k) 2.0))
121.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify1.7s

Counts

181 → 181

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	333	2626
1	831	2468
2	2409	2362
done	5000	2337

prune883.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.2b	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
0.4b	(pow n (/ (- 1.0 k) 2.0))
0.5b	(pow PI (/ (- 1.0 k) 2.0))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

13.0ms	(/ 1.0 (sqrt k))
95.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
16.0ms	(pow n (/ (- 1.0 k) 2.0))
16.0ms	(pow PI (/ (- 1.0 k) 2.0))

series963.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 1.0 (sqrt k))
778.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
85.0ms	(pow n (/ (- 1.0 k) 2.0))
50.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify2.4s

Counts

190 → 190

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	384	3225
1	1040	2900
2	3308	2698
done	5001	2678

prune996.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)))
0.4b	(pow n (/ (/ (- 1.0 k) 2.0) 2))
0.4b	(pow n (/ (/ (- 1.0 k) 2.0) 2))
0.5b	(pow PI (/ (- 1.0 k) 2.0))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

219×	`times-frac`
172×	`add-sqr-sqrt`
160×	`*-un-lft-identity`
141×	`pow-unpow`
118×	`add-cube-cbrt`
27×	`unpow-prod-down`
21×	`distribute-lft-out--` `difference-of-squares`
19×	`add-exp-log`
13×	`div-sub` `sqr-pow`
9×	`pow-to-exp` `pow-exp` `prod-exp` `div-inv` `unswap-sqr`
7×	`pow1` `swap-sqr` `associate-r` `associate-l` `pow-sub`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 249

Calls

4 calls:

54.0ms	(* (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)))
24.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
25.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
15.0ms	(pow PI (/ (- 1.0 k) 2.0))

series392.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)))
125.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
93.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
52.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify1.8s

Counts

261 → 261

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	308	4202
1	794	3385
2	2361	3282
done	5000	3187

prune1.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes177.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	28
1	18	28
done	18	28

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.2s	20743×	body	80	nan
1.8s	11900×	body	80	valid