Details

sample227.0ms

Algorithm

intervals

Results

120.0ms	654×	body	80	nan
71.0ms	362×	body	80	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2719
5	929
4	327
3	124
2	62
1	31
0	13

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt`
26×	`add-exp-log`
24×	`sqrt-prod`
16×	`unpow-prod-up`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sub-neg` `unpow-prod-down` `sqr-pow`
7×	`associate-/l*`
6×	`pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp`
3×	`pow-pow` `associate-r` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-l` `*-commutative` `div-inv` `distribute-lft-out--` `associate-/l/`

Counts

3 → 118

Calls

3 calls:

24.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
15.0ms	(* (* n 2) PI)
17.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series590.0ms

Counts

3 → 9

Calls

3 calls:

350.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
49.0ms	(* (* n 2) PI)
191.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify2.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5008
2	2241
1	662
0	271

prune557.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
36×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
24×	`sqrt-prod`
23×	`add-exp-log`
16×	`unpow-prod-up`
11×	`pow1`
8×	`sub-neg` `unpow-prod-down` `sqr-pow`
7×	`add-cbrt-cube` `prod-exp` `associate-/l*`
6×	`pow-unpow` `associate-/r*` `pow-exp`
5×	`div-exp`
4×	`pow-prod-down`
3×	`pow-pow` `associate-r` `associate-l` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr` `associate-/l/`

Counts

3 → 118

Calls

3 calls:

30.0ms	(/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))
11.0ms	(* n PI)
30.0ms	(pow (* 2 (* n PI)) (- 1/2 (/ k 2)))

series571.0ms

Counts

3 → 9

Calls

3 calls:

332.0ms	(/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))
34.0ms	(* n PI)
205.0ms	(pow (* 2 (* n PI)) (- 1/2 (/ k 2)))

simplify2.6s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	1943
1	630
0	268

prune578.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
0.2b	(/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
0.2b	(* n PI)
0.7b	(pow (* n PI) (- 1/2 (/ k 2)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
32×	`prod-exp`
28×	`add-sqr-sqrt`
22×	`pow-exp`
16×	`*-un-lft-identity`
15×	`pow-to-exp`
14×	`add-cube-cbrt`
13×	`add-cbrt-cube` `div-exp`
12×	`associate-l`
10×	`associate-r`
9×	`pow1` `pow-sub`
8×	`sqr-pow`
7×	`unpow-prod-down` `times-frac` `unswap-sqr`
6×	`unpow-prod-up` `pow-unpow` `associate-/r*` `sqrt-prod`
4×	`insert-posit16` `add-log-exp`
3×	`sub-neg` `pow-prod-down` `cbrt-unprod` `associate-/l/`
2×	`frac-times` `cbrt-undiv` `pow-pow` `associate-l/` `associate-r/` `*-commutative` `difference-of-squares`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 133

Calls

4 calls:

19.0ms	(* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
22.0ms	(/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
5.0ms	(* n PI)
8.0ms	(pow (* n PI) (- 1/2 (/ k 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

316.0ms	(* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
558.0ms	(/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
24.0ms	(* n PI)
116.0ms	(pow (* n PI) (- 1/2 (/ k 2)))

simplify2.6s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
2	2935
1	814
0	290

prune792.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
0.2b	(* n PI)
0.2b	(* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
0.7b	(pow (* n PI) (- 1/2 (/ k 2)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

170×	`times-frac`
163×	`add-sqr-sqrt`
120×	`add-exp-log`
84×	`*-un-lft-identity`
67×	`add-cube-cbrt`
62×	`div-exp`
59×	`sqrt-prod`
49×	`associate-r`
45×	`prod-exp`
41×	`sqr-pow`
36×	`unswap-sqr`
34×	`unpow-prod-up` `associate-l`
33×	`unpow-prod-down`
28×	`pow-exp`
20×	`add-cbrt-cube`
19×	`pow-to-exp`
17×	`sub-neg`
15×	`1-exp`
11×	`pow1`
7×	`associate-/l*`
6×	`pow-unpow` `associate-/r*`
5×	`cbrt-undiv` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`pow-pow` `*-commutative` `pow-sub` `difference-of-squares`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/` `distribute-lft-out--` `associate-/l/`

Counts

4 → 279

Calls

4 calls:

9.0ms	(/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
11.0ms	(* n PI)
44.0ms	(* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
8.0ms	(pow (* n PI) (- 1/2 (/ k 2)))

series998.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
36.0ms	(* n PI)
554.0ms	(* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
154.0ms	(pow (* n PI) (- 1/2 (/ k 2)))

simplify3.3s

Counts

291 → 291

Iterations

Iter	Nodes
done	5001
2	4417
1	1480
0	482

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes184.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	13

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.3s	21069×	body	80	nan
2.6s	11971×	body	80	valid
1.0ms	2×	body	160	nan