Details

sample172.0ms

Algorithm

intervals

Results

92.0ms	609×	body	80	nan
55.0ms	365×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
5	929
4	327
3	124
2	62
1	31
0	13

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize45.0ms

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

rewrite57.0ms

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:

12.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
14.0ms	(* (* n 2) PI)
28.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series663.0ms

Counts

3 → 9

Calls

3 calls:

376.0ms	(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
63.0ms	(* (* n 2) PI)
224.0ms	(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify876.0ms

Counts

127 → 127

Iterations

Iter	Nodes
done	2001
1	662
0	271

prune537.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* n 2) (sqrt PI)) (sqrt PI))
0.7b	(pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
23×	`add-exp-log`
16×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt` `sqrt-prod`
6×	`pow-unpow` `associate-r` `cbrt-unprod`
4×	`pow-pow` `pow-exp` `insert-posit16` `add-log-exp`
2×	`unpow-prod-up` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `unpow-prod-down` `times-frac` `associate-l` `*-commutative` `distribute-lft-out--` `pow-sub` `sqr-pow`

Counts

4 → 81

Calls

4 calls:

80.0ms	(* (* (* n 2) (sqrt PI)) (sqrt PI))
61.0ms	(pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2)))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series263.0ms

Counts

4 → 8

Calls

4 calls:

51.0ms	(* (* (* n 2) (sqrt PI)) (sqrt PI))
211.0ms	(pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify948.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	2001
2	1518
1	415
0	149

prune488.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* n 2) (sqrt PI))
0.7b	(pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
16×	`add-sqr-sqrt`
15×	`add-exp-log`
11×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-cube-cbrt` `sqrt-prod`
6×	`pow-unpow` `associate-r` `pow-prod-down` `prod-exp`
4×	`insert-posit16` `add-log-exp`
3×	`pow-pow` `pow-exp` `cbrt-unprod`
2×	`unpow-prod-up` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `unpow-prod-down` `times-frac` `associate-l` `*-commutative` `distribute-lft-out--` `pow-sub` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

18.0ms	(* (* n 2) (sqrt PI))
17.0ms	(pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series401.0ms

Counts

4 → 8

Calls

4 calls:

106.0ms	(* (* n 2) (sqrt PI))
295.0ms	(pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify941.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	2003
2	1301
1	366
0	136

prune572.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
19×	`add-exp-log`
16×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `pow-prod-down` `prod-exp`
9×	`sqrt-prod`
8×	`add-cube-cbrt`
6×	`pow-unpow`
5×	`pow-pow` `pow-exp`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`unpow-prod-up` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `unpow-prod-down` `times-frac` `distribute-lft-out--` `pow-sub` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

237.0ms	(pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series190.0ms

Counts

4 → 6

Calls

4 calls:

190.0ms	(pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify910.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	2002
2	996
1	319
0	129

prune437.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes227.0ms

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	18
1	18
0	15

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.0s	20622×	body	80	nan
3.3s	11847×	body	80	valid
1.0ms	2×	body	160	nan