Details

sample182.0ms

Algorithm

intervals

Results

84.0ms	760×	body	80	nan
44.0ms	432×	body	80	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	120	16
4	330	16
5	1555	16
done	5001	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

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))
1.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite173.0ms

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:

84.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
40.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
29.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series711.0ms

Counts

4 → 12

Calls

4 calls:

440.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
35.0ms	(* (* 2.0 PI) n)
44.0ms	(/ 1.0 (sqrt k))
192.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.8s

Counts

169 → 169

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	369	2880
1	1037	2720
2	4934	2550
done	5000	2548

prune667.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
0.3b	(/ 1.0 (sqrt k))
1.3b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.3b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
157×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
122×	`pow-unpow`
117×	`add-cube-cbrt`
88×	`add-exp-log`
61×	`prod-exp`
36×	`pow-exp`
18×	`distribute-lft-out--` `difference-of-squares`
16×	`pow1`
12×	`pow-to-exp` `div-sub` `sqrt-prod`
10×	`sqr-pow`
9×	`div-inv`
8×	`add-cbrt-cube`
7×	`pow-prod-down`
6×	`unpow-prod-down` `pow-pow` `associate-/r*` `pow-sub`
5×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/l*`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `associate-r/` `div-exp` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 263

Calls

4 calls:

59.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
10.0ms	(/ 1.0 (sqrt k))
32.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
42.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series846.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
66.0ms	(/ 1.0 (sqrt k))
239.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
215.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify759.0ms

Counts

275 → 275

Iterations

Useful iterations: done (746.0ms)

Iter	Nodes	Cost
0	379	5686
1	1152	4768
done	5000	4280

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
1.3b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.3b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite155.0ms

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×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `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 → 221

Calls

4 calls:

24.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
32.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
67.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series488.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* 2.0 PI) n)
47.0ms	(/ 1.0 (sqrt k))
210.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
187.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify2.4s

Counts

233 → 233

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	332	3588
1	979	3316
2	4191	3202
done	5000	3197

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
1.3b	(pow n (/ (/ (- 1.0 k) 2.0) 2))
1.3b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
151×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
115×	`add-cube-cbrt`
18×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
16×	`pow1`
12×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`div-inv`
6×	`pow-prod-down` `prod-exp` `associate-/r*`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-pow` `div-sub` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod` `associate-/l*`
2×	`pow-to-exp` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative`

Counts

4 → 219

Calls

4 calls:

28.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
14.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
51.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series431.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (* 2.0 PI) n)
40.0ms	(/ 1.0 (sqrt k))
86.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
241.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify858.0ms

Counts

231 → 231

Iterations

Useful iterations: done (847.0ms)

Iter	Nodes	Cost
0	421	3171
1	1322	2913
done	5001	2825

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes229.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	40
1	24	40
done	24	40

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.0s	20591×	body	80	nan
2.0s	11964×	body	80	valid
0.0ms	2×	body	160	nan