Details

sample157.0ms

Algorithm

intervals

Results

74.0ms	760×	body	80	nan
41.0ms	365×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1541
4	328
3	120
2	59
1	29
0	13

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

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))

rewrite138.0ms

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:

62.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
10.0ms	(/ 1.0 (sqrt k))
28.0ms	(* (* 2.0 PI) n)
29.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series807.0ms

Counts

4 → 12

Calls

4 calls:

500.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
47.0ms	(/ 1.0 (sqrt k))
64.0ms	(* (* 2.0 PI) n)
196.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.9s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	4735
1	986
0	353

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 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))

rewrite99.0ms

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:

36.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
10.0ms	(/ 1.0 (sqrt k))
16.0ms	(* n PI)
32.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

series790.0ms

Counts

4 → 12

Calls

4 calls:

502.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
72.0ms	(/ 1.0 (sqrt k))
40.0ms	(* n PI)
176.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

simplify2.9s

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	4063
1	961
0	352

prune948.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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))

rewrite62.0ms

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:

27.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))
5.0ms	(/ 1.0 (sqrt k))
6.0ms	(* n PI)
17.0ms	(pow (* n PI) (/ (- 1.0 k) 2.0))

series592.0ms

Counts

4 → 12

Calls

4 calls:

389.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))
40.0ms	(/ 1.0 (sqrt k))
38.0ms	(* n PI)
125.0ms	(pow (* n PI) (/ (- 1.0 k) 2.0))

simplify3.1s

Counts

146 → 146

Iterations

Iter	Nodes
done	5001
2	3699
1	891
0	332

prune944.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

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)

rewrite97.0ms

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:

28.0ms	(* (* n (sqrt PI)) (sqrt PI))
64.0ms	(pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series195.0ms

Counts

4 → 8

Calls

4 calls:

28.0ms	(* (* n (sqrt PI)) (sqrt PI))
167.0ms	(pow (* 2.0 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1.0 k) 2.0))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify1.7s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1949
1	459
0	165

prune479.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes203.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.6s	20608×	body	80	nan
2.3s	11771×	body	80	valid