Details

sample181.0ms

Algorithm

intervals

Results

92.0ms	760×	body	80	nan
43.0ms	365×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	2693
5	806
4	285
3	114
2	58
1	29
0	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
8×	`associate-r`
6×	`associate-/r*` `div-exp` `pow-prod-down` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 149

Calls

4 calls:

46.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(/ 1.0 (sqrt k))
21.0ms	(* (* 2.0 PI) n)
33.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series730.0ms

Counts

4 → 12

Calls

4 calls:

405.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
56.0ms	(/ 1.0 (sqrt k))
64.0ms	(* (* 2.0 PI) n)
204.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify3.0s

Counts

161 → 161

Iterations

Iter	Nodes
done	5001
2	3261
1	975
0	353

prune934.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* n PI)
0.9b	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
55×	`times-frac`
50×	`*-un-lft-identity`
44×	`add-cube-cbrt`
43×	`add-exp-log`
25×	`associate-l`
23×	`sqrt-prod`
20×	`prod-exp`
19×	`pow-unpow`
13×	`add-cbrt-cube`
12×	`pow1`
9×	`pow-exp`
8×	`associate-r`
7×	`unswap-sqr`
6×	`associate-/r*` `div-exp`
5×	`sqr-pow`
4×	`pow-prod-down` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 149

Calls

4 calls:

38.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
9.0ms	(/ 1.0 (sqrt k))
8.0ms	(* n PI)
15.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

series818.0ms

Counts

4 → 12

Calls

4 calls:

505.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
55.0ms	(/ 1.0 (sqrt k))
39.0ms	(* n PI)
219.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

simplify2.6s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	3115
1	954
0	352

prune913.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* n PI)
0.8b	(pow (* n PI) (/ (- 1.0 k) 2.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
33×	`times-frac` `add-cube-cbrt`
31×	`add-exp-log`
19×	`pow-unpow`
17×	`prod-exp`
12×	`pow-exp` `sqrt-prod`
10×	`add-cbrt-cube` `associate-l`
9×	`pow1`
8×	`pow-to-exp` `associate-r` `sqr-pow`
7×	`unpow-prod-down` `unswap-sqr`
6×	`associate-/r*`
5×	`div-sub` `pow-sub`
4×	`add-log-exp`
3×	`pow-prod-down` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`pow-pow` `*-commutative` `cbrt-unprod` `div-inv`
1×	`frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-l/` `associate-r/`

Counts

4 → 134

Calls

4 calls:

24.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))
10.0ms	(/ 1.0 (sqrt k))
10.0ms	(* n PI)
13.0ms	(pow (* n PI) (/ (- 1.0 k) 2.0))

series604.0ms

Counts

4 → 12

Calls

4 calls:

388.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))
54.0ms	(/ 1.0 (sqrt k))
27.0ms	(* n PI)
135.0ms	(pow (* n PI) (/ (- 1.0 k) 2.0))

simplify3.2s

Counts

146 → 146

Iterations

Iter	Nodes
done	5003
2	2836
1	888
0	332

prune883.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* n (sqrt PI)) (sqrt PI))
0.9b	(pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`pow1`
19×	`pow-unpow` `add-exp-log`
17×	`add-cube-cbrt`
15×	`times-frac`
9×	`add-cbrt-cube` `pow-prod-down` `prod-exp` `sqrt-prod`
6×	`associate-r`
4×	`pow-pow` `pow-exp` `add-log-exp`
3×	`cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

19.0ms	(* (* n (sqrt PI)) (sqrt PI))
101.0ms	(pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series219.0ms

Counts

4 → 8

Calls

4 calls:

32.0ms	(* (* n (sqrt PI)) (sqrt PI))
187.0ms	(pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify2.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1473
1	454
0	165

prune491.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes352.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.4s	20608×	body	80	nan
2.2s	11771×	body	80	valid