Details

sample184.0ms

Algorithm

intervals

Results

104.0ms	619×	body	80	nan
55.0ms	386×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

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))
1.1b	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

rewrite92.0ms

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:

25.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
20.0ms	(* PI (* n 2))
24.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

series530.0ms

Counts

3 → 9

Calls

3 calls:

281.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
35.0ms	(* PI (* n 2))
212.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

simplify2.7s

Counts

445 → 445

Iterations

Iter	Nodes
2	4287
1	1515
0	698

prune5.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
0.2b	(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
0.2b	(* PI (* n 2))
1.1b	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

3088×	`times-frac`
1878×	`add-sqr-sqrt`
1875×	`*-un-lft-identity`
1873×	`add-cube-cbrt`
1312×	`unpow-prod-up`
1248×	`prod-diff`
693×	`sqrt-prod`
327×	`associate-/r*`
102×	`div-inv`
72×	`add-exp-log`
32×	`sub-neg` `unpow-prod-down` `div-exp` `sqr-pow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
6×	`rec-exp` `pow-unpow` `1-exp` `pow-prod-down` `associate-/r/` `pow-sub`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`associate-r` `*-commutative` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 1599

Calls

4 calls:

39.0ms	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
13.0ms	(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
13.0ms	(* PI (* n 2))
26.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

series944.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
378.0ms	(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
37.0ms	(* PI (* n 2))
224.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

simplify3.1m

Counts

1611 → 1611

Iterations

Iter	Nodes
1	4705
0	1731

prune29.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))
0.2b	(/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))
0.5b	(pow PI (- 1/2 (/ k 2)))
1.1b	(pow (* n 2) (- 1/2 (/ k 2)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

1242×	`times-frac`
973×	`add-sqr-sqrt`
893×	`*-un-lft-identity`
874×	`add-cube-cbrt`
738×	`unpow-prod-up`
702×	`prod-diff`
293×	`sqrt-prod`
281×	`associate-r`
156×	`add-exp-log`
149×	`associate-l`
74×	`div-exp`
62×	`prod-exp`
57×	`div-inv`
46×	`associate-/r*`
42×	`sqr-pow`
40×	`pow-exp`
36×	`unpow-prod-down`
35×	`unswap-sqr`
28×	`pow-to-exp`
18×	`sub-neg` `add-cbrt-cube`
15×	`rec-exp` `1-exp`
12×	`pow-unpow`
10×	`pow1`
6×	`associate-/l*`
5×	`cbrt-undiv` `pow-sub`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-pow` `associate-/r/`
2×	`pow-prod-down` `distribute-lft-out--`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 1011

Calls

4 calls:

94.0ms	(* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))
11.0ms	(/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))
7.0ms	(pow PI (- 1/2 (/ k 2)))
16.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

448.0ms	(* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))
187.0ms	(/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))
56.0ms	(pow PI (- 1/2 (/ k 2)))
558.0ms	(pow (* n 2) (- 1/2 (/ k 2)))

simplify3.4s

Counts

1023 → 1023

Iterations

Iter	Nodes
1	3971
0	1264

prune14.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* 1 (/ 1 (pow n (- 1/2 (/ k 2))))) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow 2 (- 1/2 (/ k 2)))))
0.2b	(/ (sqrt k) (pow 2 (- 1/2 (/ k 2))))
0.5b	(pow PI (- 1/2 (/ k 2)))
0.8b	(pow n (- 1/2 (/ k 2)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

1064×	`times-frac`
939×	`add-exp-log`
804×	`add-sqr-sqrt`
780×	`*-un-lft-identity`
776×	`add-cube-cbrt`
656×	`unpow-prod-up`
624×	`prod-diff`
591×	`div-exp`
496×	`prod-exp`
294×	`sqrt-prod`
293×	`associate-r`
223×	`pow-to-exp` `pow-exp`
192×	`1-exp`
72×	`rec-exp`
53×	`associate-l`
51×	`div-inv`
50×	`unpow-prod-down`
48×	`associate-/r*`
38×	`add-cbrt-cube`
18×	`sqr-pow`
16×	`sub-neg`
13×	`cbrt-undiv`
12×	`pow-unpow` `cbrt-unprod`
8×	`pow1`
7×	`unswap-sqr`
6×	`associate-/l*`
5×	`pow-sub`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`associate-/r/`
2×	`pow-pow` `distribute-lft-out--`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 1122

Calls

4 calls:

68.0ms	(* (/ (* 1 (/ 1 (pow n (- 1/2 (/ k 2))))) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow 2 (- 1/2 (/ k 2)))))
17.0ms	(/ (sqrt k) (pow 2 (- 1/2 (/ k 2))))
6.0ms	(pow PI (- 1/2 (/ k 2)))
7.0ms	(pow n (- 1/2 (/ k 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

669.0ms	(* (/ (* 1 (/ 1 (pow n (- 1/2 (/ k 2))))) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow 2 (- 1/2 (/ k 2)))))
287.0ms	(/ (sqrt k) (pow 2 (- 1/2 (/ k 2))))
59.0ms	(pow PI (- 1/2 (/ k 2)))
69.0ms	(pow n (- 1/2 (/ k 2)))

simplify4.5s

Counts

1134 → 1134

Iterations

Iter	Nodes
1	4422
0	1432

prune15.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	20
1	20
0	18

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.6s	20785×	body	80	nan
1.7s	11867×	body	80	valid
1.0ms	3×	body	160	nan