Details

sample178.0ms

Algorithm

intervals

Results

72.0ms	648×	body	80	nan
47.0ms	378×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize17.0ms

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	(/ 1.0 (sqrt k))
0.2b	(* (* 2.0 PI) n)
1.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite160.0ms

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:

59.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(/ 1.0 (sqrt k))
35.0ms	(* (* 2.0 PI) n)
46.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series733.0ms

Counts

4 → 12

Calls

4 calls:

447.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
47.0ms	(/ 1.0 (sqrt k))
50.0ms	(* (* 2.0 PI) n)
189.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.9s

Counts

169 → 169

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	369	2880
1	1037	2720
2	4907	2552
done	5000	2549

prune675.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
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))
1.6b	(pow n (/ (- 1.0 k) 2.0))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
48×	`times-frac`
41×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
16×	`prod-exp`
13×	`pow-exp`
12×	`sqrt-prod`
10×	`unpow-prod-down`
9×	`pow-to-exp` `sqr-pow`
8×	`pow1` `add-cbrt-cube`
7×	`associate-r`
6×	`div-sub` `associate-/r*` `distribute-lft-out--` `pow-sub` `difference-of-squares` `unswap-sqr`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-inv` `associate-/l*`
2×	`pow-prod-down`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `associate-r/` `div-exp` `associate-l/` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt k))
36.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
20.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
8.0ms	(pow n (/ (- 1.0 k) 2.0))

series663.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (sqrt k))
430.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
96.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
93.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

170 → 170

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	324	2568
1	882	2345
2	3444	2252
done	5002	2234

prune928.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
0.5b	(pow PI (/ (- 1.0 k) 2.0))
1.6b	(pow n (/ (- 1.0 k) 2.0))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
57×	`prod-exp`
53×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
41×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`pow-to-exp` `pow-exp`
14×	`div-sub` `pow-sub`
12×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`unpow-prod-down`
7×	`associate-r`
6×	`pow1` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `cbrt-unprod` `div-inv` `associate-/l` `sqr-pow`
2×	`pow-pow` `pow-prod-down`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative`

Counts

4 → 171

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt k))
60.0ms	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
11.0ms	(pow PI (/ (- 1.0 k) 2.0))
15.0ms	(pow n (/ (- 1.0 k) 2.0))

series734.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1.0 (sqrt k))
520.0ms	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
62.0ms	(pow PI (/ (- 1.0 k) 2.0))
85.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

183 → 183

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	367	3160
1	1052	2810
2	4277	2450
done	5000	2440

prune836.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

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)))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
1.6b	(pow n (/ (- 1.0 k) 2.0))

rewrite106.0ms

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))
63.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
13.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
8.0ms	(pow n (/ (- 1.0 k) 2.0))

series693.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ 1.0 (sqrt k))
404.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
111.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
114.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

181 → 181

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	333	2626
1	927	2468
2	3726	2362
done	5000	2340

prune920.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes205.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.0s	20845×	body	80	nan
2.2s	11893×	body	80	valid
1.0ms	3×	body	160	nan