Details

sample156.0ms

Algorithm

intervals

Results

53.0ms	638×	body	80	nan
53.0ms	386×	body	80	valid

simplify6.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
6	2792
5	816
4	285
3	114
2	58
1	29
0	13

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize54.0ms

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

rewrite212.0ms

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` `insert-posit16` `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 → 161

Calls

4 calls:

99.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
25.0ms	(* (* 2.0 PI) n)
17.0ms	(/ 1.0 (sqrt k))
47.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

765.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
70.0ms	(* (* 2.0 PI) n)
83.0ms	(/ 1.0 (sqrt k))
283.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify6.7s

Counts

173 → 173

Iterations

Iter	Nodes
done	5001
2	3368
1	1014
0	365

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite233.0ms

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×	`associate-/r*` `pow-pow` `pow-exp`
4×	`expm1-log1p-u` `div-sub` `insert-posit16` `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` `clear-num` `frac-2neg` `div-exp` `associate-l` `*-commutative`

Counts

4 → 225

Calls

4 calls:

30.0ms	(* (* 2.0 PI) n)
17.0ms	(/ 1.0 (sqrt k))
74.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
70.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series677.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* 2.0 PI) n)
75.0ms	(/ 1.0 (sqrt k))
261.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
282.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify4.9s

Counts

237 → 237

Iterations

Iter	Nodes
done	5006
2	2642
1	954
0	337

prune3.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
0.8b	(pow n (/ (- 1.0 k) 2.0))

rewrite95.0ms

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×	`associate-/r*` `div-sub` `distribute-lft-out--` `pow-sub` `difference-of-squares` `unswap-sqr`
5×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-inv` `associate-/l*`
2×	`pow-prod-down`
1×	`frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-l/` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 162

Calls

4 calls:

32.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
12.0ms	(/ 1.0 (sqrt k))
15.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
20.0ms	(pow n (/ (- 1.0 k) 2.0))

series859.0ms

Counts

4 → 12

Calls

4 calls:

530.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
63.0ms	(/ 1.0 (sqrt k))
132.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
133.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify5.5s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
2	2550
1	845
0	323

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow PI (/ (- 1.0 k) 2.0))
0.8b	(pow n (/ (- 1.0 k) 2.0))

rewrite172.0ms

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-l`
6×	`pow1` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
5×	`frac-times` `associate-*r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l/` `cbrt-unprod` `div-inv` `associate-/l` `sqr-pow`
2×	`pow-pow` `pow-prod-down`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-r` `*-commutative`

Counts

4 → 175

Calls

4 calls:

102.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
8.0ms	(/ 1.0 (sqrt k))
10.0ms	(pow PI (/ (- 1.0 k) 2.0))
21.0ms	(pow n (/ (- 1.0 k) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
76.0ms	(/ 1.0 (sqrt k))
101.0ms	(pow PI (/ (- 1.0 k) 2.0))
141.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify7.1s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
2	3249
1	1007
0	371

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.2s	20923×	body	80	nan
1.5s	11902×	body	80	valid