Details

sample123.0ms

Algorithm

intervals

Results

61.0ms	677×	body	80	nan
36.0ms	373×	body	80	valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2753
5	970
4	328
3	124
2	62
1	31
0	13

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
0.2b	(* (* n 2) PI)
0.9b	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

493×	`times-frac`
383×	`add-sqr-sqrt`
380×	`*-un-lft-identity`
378×	`add-cube-cbrt`
328×	`unpow-prod-up`
312×	`prod-diff`
141×	`sqrt-prod`
46×	`associate-/l*`
26×	`add-exp-log`
25×	`div-inv`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sub-neg` `unpow-prod-down` `sqr-pow`
6×	`pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp`
3×	`expm1-log1p-u` `pow-pow` `associate-r` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-l` `*-commutative` `distribute-lft-out--` `associate-/l/`

Counts

3 → 436

Calls

3 calls:

72.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
34.0ms	(* (* n 2) PI)
35.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series593.0ms

Counts

3 → 9

Calls

3 calls:

354.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
39.0ms	(* (* n 2) PI)
200.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify3.7s

Counts

445 → 445

Iterations

Iter	Nodes
done	5000
2	4377
1	1539
0	699

prune3.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow PI (- 1/2 (* k 1/2))) (sqrt k))
0.2b	(* (pow (* 2 n) (- 1/2 (* k 1/2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k)))
0.5b	(pow PI (- 1/2 (* k 1/2)))
0.6b	(pow (* 2 n) (- 1/2 (* k 1/2)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
130×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
101×	`add-cube-cbrt`
81×	`sqrt-prod`
80×	`unpow-prod-up`
76×	`associate-r`
53×	`add-exp-log`
48×	`unpow-prod-down` `prod-diff`
27×	`sqr-pow`
21×	`prod-exp`
16×	`sub-neg` `pow-exp`
15×	`div-exp`
14×	`unswap-sqr`
12×	`associate-/l*`
11×	`pow-to-exp` `add-cbrt-cube`
10×	`associate-l`
8×	`pow1` `pow-unpow`
6×	`associate-/r*`
5×	`pow-sub`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow`
2×	`cbrt-undiv` `distribute-rgt-out--` `cbrt-unprod` `div-inv`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 294

Calls

4 calls:

28.0ms	(/ (pow PI (- 1/2 (* k 1/2))) (sqrt k))
92.0ms	(* (pow (* 2 n) (- 1/2 (* k 1/2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k)))
11.0ms	(pow PI (- 1/2 (* k 1/2)))
19.0ms	(pow (* 2 n) (- 1/2 (* k 1/2)))

series936.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ (pow PI (- 1/2 (* k 1/2))) (sqrt k))
535.0ms	(* (pow (* 2 n) (- 1/2 (* k 1/2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k)))
56.0ms	(pow PI (- 1/2 (* k 1/2)))
131.0ms	(pow (* 2 n) (- 1/2 (* k 1/2)))

simplify3.1s

Counts

306 → 306

Iterations

Iter	Nodes
done	5000
1	1412
0	492

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (log PI) (- 1/2 (* k 1/2)))
0.2b	(/ (exp (* (log PI) (- 1/2 (* k 1/2)))) (sqrt k))
0.2b	(* (pow (* 2 n) (- 1/2 (* k 1/2))) (/ (exp (* (log PI) (- 1/2 (* k 1/2)))) (sqrt k)))
0.6b	(pow (* 2 n) (- 1/2 (* k 1/2)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

160×	`times-frac`
130×	`exp-sum`
121×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
106×	`add-cube-cbrt`
90×	`prod-diff`
86×	`associate-r`
83×	`sqrt-prod`
70×	`distribute-rgt-in` `distribute-lft-in`
30×	`sub-neg`
26×	`add-exp-log`
14×	`associate-l`
13×	`add-cbrt-cube` `associate-/l*`
12×	`prod-exp`
10×	`pow1` `unpow-prod-up`
7×	`unswap-sqr`
6×	`associate-/r*` `pow-exp`
5×	`div-exp` `sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-*r/` `cbrt-unprod` `pow-sub`
2×	`cbrt-undiv` `unpow-prod-down` `pow-pow` `distribute-rgt-out--` `pow-prod-down` `*-commutative` `div-inv`
1×	`frac-times` `clear-num` `frac-2neg` `flip3--` `associate-*l/` `log-pow` `flip--`

Counts

4 → 296

Calls

4 calls:

23.0ms	(* (log PI) (- 1/2 (* k 1/2)))
25.0ms	(/ (exp (* (log PI) (- 1/2 (* k 1/2)))) (sqrt k))
97.0ms	(* (pow (* 2 n) (- 1/2 (* k 1/2))) (/ (exp (* (log PI) (- 1/2 (* k 1/2)))) (sqrt k)))
18.0ms	(pow (* 2 n) (- 1/2 (* k 1/2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

411.0ms	(* (log PI) (- 1/2 (* k 1/2)))
197.0ms	(/ (exp (* (log PI) (- 1/2 (* k 1/2)))) (sqrt k))
450.0ms	(* (pow (* 2 n) (- 1/2 (* k 1/2))) (/ (exp (* (log PI) (- 1/2 (* k 1/2)))) (sqrt k)))
119.0ms	(pow (* 2 n) (- 1/2 (* k 1/2)))

simplify3.4s

Counts

308 → 308

Iterations

Iter	Nodes
done	5001
1	1444
0	513

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow n (- 1/2 (* k 1/2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k)))
0.3b	(* (pow 2 (- 1/2 (* k 1/2))) (* (pow n (- 1/2 (* k 1/2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k))))
0.5b	(pow PI (- 1/2 (* k 1/2)))
0.6b	(pow n (- 1/2 (* k 1/2)))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

139×	`add-exp-log`
106×	`add-sqr-sqrt`
90×	`times-frac`
87×	`prod-exp`
77×	`associate-r`
61×	`*-un-lft-identity`
59×	`add-cube-cbrt`
50×	`unpow-prod-up`
45×	`sqrt-prod`
43×	`pow-to-exp` `unpow-prod-down` `pow-exp`
36×	`div-exp`
30×	`prod-diff`
24×	`associate-l`
23×	`sqr-pow`
21×	`unswap-sqr`
18×	`add-cbrt-cube`
12×	`pow-sub`
10×	`sub-neg`
8×	`pow-unpow`
7×	`cbrt-unprod`
6×	`frac-times` `pow1` `associate-*r/`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-pow` `distribute-rgt-out--` `*-commutative`
1×	`div-inv`

Counts

4 → 264

Calls

4 calls:

77.0ms	(* (pow n (- 1/2 (* k 1/2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k)))
102.0ms	(* (pow 2 (- 1/2 (* k 1/2))) (* (pow n (- 1/2 (* k 1/2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k))))
10.0ms	(pow PI (- 1/2 (* k 1/2)))
10.0ms	(pow n (- 1/2 (* k 1/2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

364.0ms	(* (pow n (- 1/2 (* k 1/2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k)))
825.0ms	(* (pow 2 (- 1/2 (* k 1/2))) (* (pow n (- 1/2 (* k 1/2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k))))
68.0ms	(pow PI (- 1/2 (* k 1/2)))
106.0ms	(pow n (- 1/2 (* k 1/2)))

simplify2.9s

Counts

276 → 276

Iterations

Iter	Nodes
done	5000
1	1466
0	485

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes104.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.8s	20838×	body	80	nan
1.8s	11857×	body	80	valid
0.0ms	1×	body	160	nan