Details

sample154.0ms

Algorithm

intervals

Results

69.0ms	608×	body	80	nan
46.0ms	355×	body	80	valid

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	119	16
4	313	16
5	843	16
6	3221	16
done	5001	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

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

rewrite155.0ms

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:

65.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
25.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
45.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series776.0ms

Counts

4 → 12

Calls

4 calls:

441.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
58.0ms	(* (* 2.0 PI) n)
61.0ms	(/ 1.0 (sqrt k))
215.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

161 → 161

Iterations

Useful iterations: 2 (822.0ms)

Iter	Nodes	Cost
0	361	2800
1	931	2635
2	3051	2471
done	5001	2471

prune723.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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))

rewrite100.0ms

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×	`pow-to-exp` `div-sub` `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 → 161

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt k))
50.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
23.0ms	(pow n (/ (- 1.0 k) 2.0))
12.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series721.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1.0 (sqrt k))
441.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
107.0ms	(pow n (/ (- 1.0 k) 2.0))
121.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify1.7s

Counts

173 → 173

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	325	2550
1	807	2394
2	2346	2288
done	5001	2206

prune722.0ms

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))

rewrite138.0ms

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×	`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 → 170

Calls

4 calls:

8.0ms	(/ 1.0 (sqrt k))
83.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
13.0ms	(pow n (/ (- 1.0 k) 2.0))
16.0ms	(pow PI (/ (- 1.0 k) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1.0 (sqrt k))
880.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
123.0ms	(pow n (/ (- 1.0 k) 2.0))
65.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify2.1s

Counts

182 → 182

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	376	3141
1	1009	2818
2	3225	2638
done	5000	2624

prune994.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

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))

rewrite105.0ms

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×	`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 → 241

Calls

4 calls:

28.0ms	(* (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)))
21.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
15.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
16.0ms	(pow PI (/ (- 1.0 k) 2.0))

series399.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)))
123.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
96.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
75.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify2.0s

Counts

253 → 253

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	302	4106
1	783	3317
2	2320	3213
done	5001	3116

prune2.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes233.0ms

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

sample5.8s

Algorithm

intervals

Results

3.0s	20743×	body	80	nan
1.9s	11900×	body	80	valid