Details

sample110.0ms

Algorithm

intervals

Results

38.0ms	584×	body	80	nan
37.0ms	363×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	120	16
4	330	16
5	1545	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 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)
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite186.0ms

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×	`div-exp` `pow-prod-down` `associate-/r*` `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` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 149

Calls

4 calls:

77.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
12.0ms	(/ 1.0 (sqrt k))
42.0ms	(* (* 2.0 PI) n)
42.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series775.0ms

Counts

4 → 12

Calls

4 calls:

459.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
52.0ms	(/ 1.0 (sqrt k))
42.0ms	(* (* 2.0 PI) n)
223.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.6s

Counts

161 → 161

Iterations

Useful iterations: 2 (917.0ms)

Iter	Nodes	Cost
0	361	2800
1	1008	2643
2	4735	2473
done	5001	2473

prune710.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
0.3b	(* (* 2.0 PI) n)
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
23×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`times-frac`
19×	`pow-unpow`
17×	`add-cube-cbrt`
14×	`pow1` `prod-exp`
13×	`add-cbrt-cube`
6×	`div-exp` `pow-prod-down` `pow-exp` `associate-/r*` `sqrt-prod`
4×	`cbrt-unprod`
3×	`pow-pow` `associate-r` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`cbrt-undiv` `pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`unpow-prod-down` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative` `associate-/l/` `associate-/l*` `sqr-pow`

Counts

3 → 86

Calls

3 calls:

24.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
30.0ms	(* (* 2.0 PI) n)
26.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series639.0ms

Counts

3 → 9

Calls

3 calls:

405.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
61.0ms	(* (* 2.0 PI) n)
172.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

95 → 95

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	264	1828
1	749	1703
2	3493	1533
done	5000	1531

prune419.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
1.1b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.1b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
143×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
122×	`pow-unpow`
103×	`add-cube-cbrt`
91×	`add-exp-log`
64×	`prod-exp`
36×	`pow-exp`
21×	`pow1`
18×	`distribute-lft-out--` `difference-of-squares`
12×	`pow-to-exp` `div-sub`
11×	`add-cbrt-cube`
10×	`pow-prod-down` `sqr-pow`
8×	`associate-r` `div-inv`
6×	`unpow-prod-down` `pow-pow` `associate-l` `pow-sub`
5×	`swap-sqr`
4×	`cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`*-commutative`
1×	`pow2` `frac-times` `associate-r/` `associate-l/` `pow-sqr` `pow-prod-up`

Counts

4 → 234

Calls

4 calls:

20.0ms	(* (* 2.0 PI) n)
74.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
43.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
55.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series773.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* 2.0 PI) n)
280.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
214.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
233.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify769.0ms

Counts

246 → 246

Iterations

Useful iterations: done (758.0ms)

Iter	Nodes	Cost
0	313	5306
1	1017	4459
done	5000	3965

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

38×	`pow-unpow`
36×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
26×	`pow1` `add-exp-log`
24×	`add-cube-cbrt`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
6×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
4×	`add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

36.0ms	(* (* 2.0 PI) n)
22.0ms	(* (* 2.0 PI) n)
30.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
23.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series557.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (* 2.0 PI) n)
52.0ms	(* (* 2.0 PI) n)
207.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
233.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.5s

Counts

120 → 120

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	149	1624
1	428	1526
2	2085	1402
done	5001	1394

prune662.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes147.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	16	16
done	16	16

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.9s	20706×	body	80	nan
2.1s	11991×	body	80	valid
0.0ms	1×	body	160	nan