Details

sample137.0ms

Algorithm

intervals

Results

56.0ms	656×	body	80	nan
35.0ms	358×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1551
4	328
3	120
2	59
1	29
0	13

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
1.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite109.0ms

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×	`associate-/r*` `div-exp` `pow-prod-down` `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` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 157

Calls

4 calls:

54.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
8.0ms	(/ 1.0 (sqrt k))
18.0ms	(* (* 2.0 PI) n)
18.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series765.0ms

Counts

4 → 12

Calls

4 calls:

433.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
43.0ms	(/ 1.0 (sqrt k))
54.0ms	(* (* 2.0 PI) n)
234.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify4.2s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	4865
1	1013
0	361

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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))
1.2b	(pow n (/ (- 1.0 k) 2.0))

rewrite80.0ms

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×	`add-cbrt-cube` `prod-exp`
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` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 169

Calls

4 calls:

32.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
5.0ms	(/ 1.0 (sqrt k))
23.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
7.0ms	(pow n (/ (- 1.0 k) 2.0))

series753.0ms

Counts

4 → 12

Calls

4 calls:

443.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
69.0ms	(/ 1.0 (sqrt k))
123.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
117.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.7s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	3775
1	928
0	334

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt k))
0.3b	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))
0.5b	(pow PI (/ (- 1.0 k) 2.0))
1.2b	(pow n (/ (- 1.0 k) 2.0))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
72×	`times-frac`
66×	`*-un-lft-identity`
54×	`add-cube-cbrt`
38×	`pow-unpow`
24×	`sqrt-prod`
22×	`associate-l`
21×	`add-exp-log`
12×	`unpow-prod-down`
11×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-r`
6×	`pow1` `associate-/r*` `prod-exp` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
4×	`expm1-log1p-u` `pow-to-exp` `div-sub` `div-exp` `pow-exp` `log1p-expm1-u` `div-inv` `pow-sub` `add-log-exp`
3×	`associate-/l*`
2×	`cbrt-undiv` `pow-pow` `cbrt-unprod`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 172

Calls

4 calls:

10.0ms	(/ 1.0 (sqrt k))
47.0ms	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))
19.0ms	(pow PI (/ (- 1.0 k) 2.0))
13.0ms	(pow n (/ (- 1.0 k) 2.0))

series524.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ 1.0 (sqrt k))
266.0ms	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))
83.0ms	(pow PI (/ (- 1.0 k) 2.0))
115.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.7s

Counts

184 → 184

Iterations

Iter	Nodes
done	5000
2	4088
1	973
0	353

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
1.2b	(pow n (/ (- 1.0 k) 2.0))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

57×	`pow-unpow`
50×	`add-sqr-sqrt` `pow1` `*-un-lft-identity`
45×	`times-frac`
32×	`sqrt-div` `add-cube-cbrt`
26×	`pow-prod-down`
23×	`add-exp-log`
19×	`div-sub` `pow-sub`
17×	`frac-times`
16×	`add-cbrt-cube`
12×	`pow1/2`
11×	`associate-l/` `associate-r/`
10×	`prod-exp`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`cbrt-unprod`
5×	`unpow-prod-down` `pow-pow` `sqrt-unprod` `pow-exp` `pow-sqr` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `div-inv` `sqr-pow`
2×	`pow-plus`
1×	`pow2` `rem-square-sqrt` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

4 → 164

Calls

4 calls:

180.0ms	(* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))))
14.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
14.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
7.0ms	(pow n (/ (- 1.0 k) 2.0))

series878.0ms

Counts

4 → 12

Calls

4 calls:

563.0ms	(* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))))
104.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
103.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
107.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.7s

Counts

176 → 176

Iterations

Iter	Nodes
done	5001
2	3531
1	842
0	281

prune1.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes470.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.8s	20122×	body	80	nan
1.5s	11872×	body	80	valid