Details

sample212.0ms

Algorithm

intervals

Results

115.0ms	621×	body	80	nan
65.0ms	359×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
6	2053
5	821
4	322
3	123
2	60
1	29
0	13

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
0.2b	(* PI (* n 2))
1.6b	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

rewrite111.0ms

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-l` `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-r` `*-commutative` `distribute-lft-out--` `associate-/l/`

Counts

3 → 436

Calls

3 calls:

34.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
27.0ms	(* PI (* n 2))
24.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

series567.0ms

Counts

3 → 9

Calls

3 calls:

334.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
35.0ms	(* PI (* n 2))
198.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

simplify3.3s

Counts

445 → 445

Iterations

Iter	Nodes
2	4287
1	1515
0	698

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
0.2b	(/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
0.4b	(pow PI (- 1/2 (/ k 2)))
1.3b	(pow (* n 2) (- 1/2 (/ k 2)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

1442×	`times-frac`
1083×	`add-sqr-sqrt`
1077×	`*-un-lft-identity`
1073×	`add-cube-cbrt`
902×	`unpow-prod-up`
864×	`sqrt-prod`
858×	`prod-diff`
94×	`associate-/l*`
68×	`div-inv`
44×	`unpow-prod-down`
22×	`sub-neg` `sqr-pow`
21×	`add-exp-log`
18×	`associate-/r*`
12×	`pow-unpow`
8×	`pow1` `add-cbrt-cube`
7×	`div-exp`
6×	`pow-exp`
4×	`expm1-log1p-u` `pow-to-exp` `insert-posit16` `log1p-expm1-u` `pow-sub` `add-log-exp` `difference-of-squares`
3×	`pow-pow`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `prod-exp` `distribute-lft-out--` `associate-/l/`
1×	`pow-prod-down`

Counts

4 → 1125

Calls

4 calls:

16.0ms	(/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
34.0ms	(/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
13.0ms	(pow PI (- 1/2 (/ k 2)))
19.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

series675.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
253.0ms	(/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
60.0ms	(pow PI (- 1/2 (/ k 2)))
134.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

simplify2.3s

Counts

1137 → 1137

Iterations

Iter	Nodes
1	2440
0	1350

prune8.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))
0.2b	(/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
0.4b	(pow PI (- 1/2 (/ k 2)))
1.3b	(pow (* n 2) (- 1/2 (/ k 2)))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

4643×	`times-frac`
2828×	`add-sqr-sqrt`
2822×	`*-un-lft-identity`
2818×	`add-cube-cbrt`
2097×	`sqrt-prod`
1968×	`unpow-prod-up`
1872×	`prod-diff`
428×	`associate-/r*`
150×	`div-inv`
70×	`unpow-prod-down`
51×	`associate-/l*`
48×	`sub-neg` `sqr-pow`
45×	`add-exp-log`
25×	`div-exp`
12×	`pow-unpow`
11×	`add-cbrt-cube`
10×	`pow-exp`
9×	`pow1`
7×	`pow-sub`
6×	`pow-to-exp`
5×	`rec-exp` `1-exp` `associate-/r/`
4×	`expm1-log1p-u` `cbrt-undiv` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-pow`
2×	`clear-num` `frac-2neg` `distribute-lft-out--`
1×	`pow-prod-down` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 2349

Calls

4 calls:

28.0ms	(/ 1 (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))
13.0ms	(/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
7.0ms	(pow PI (- 1/2 (/ k 2)))
10.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

series667.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ 1 (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))
240.0ms	(/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
65.0ms	(pow PI (- 1/2 (/ k 2)))
146.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

simplify2.8m

Counts

2361 → 2361

Iterations

Iter	Nodes
1	6466
0	2609

prune8.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow PI (- 1/2 (/ k 2)))
0.6b	(cbrt k)
0.6b	(cbrt k)
1.3b	(pow (* n 2) (- 1/2 (/ k 2)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
82×	`unpow-prod-up`
81×	`*-un-lft-identity`
78×	`prod-diff`
77×	`add-cube-cbrt`
56×	`times-frac`
12×	`pow-unpow`
8×	`pow1` `add-exp-log`
6×	`cbrt-prod` `div-inv`
4×	`expm1-log1p-u` `unpow-prod-down` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-pow` `pow-exp`
2×	`pow-to-exp` `sub-neg` `pow1/3` `distribute-lft-out--` `pow-sub` `sqr-pow`
1×	`pow-prod-down` `prod-exp`

Counts

4 → 158

Calls

4 calls:

6.0ms	(pow PI (- 1/2 (/ k 2)))
1.0ms	(cbrt k)
1.0ms	(cbrt k)
9.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow PI (- 1/2 (/ k 2)))
184.0ms	(cbrt k)
180.0ms	(cbrt k)
85.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

simplify1.2s

Counts

170 → 170

Iterations

Iter	Nodes
2	3002
1	1131
0	371

prune945.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes165.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	19
1	19
0	17

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.7s	20592×	body	80	nan
1.9s	11910×	body	80	valid
0.0ms	1×	body	160	nan