Details

sample92.0ms

Algorithm

intervals

Results

35.0ms	676×	body	80	nan
26.0ms	374×	body	80	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1034	8
5	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

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:

39.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
8.0ms	(/ 1.0 (sqrt k))
20.0ms	(* (* 2.0 PI) n)
22.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series486.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
37.0ms	(/ 1.0 (sqrt k))
28.0ms	(* (* 2.0 PI) n)
125.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5002	1344

prune423.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

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:

22.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
19.0ms	(* (* 2.0 PI) n)
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series423.0ms

Counts

3 → 9

Calls

3 calls:

263.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
33.0ms	(* (* 2.0 PI) n)
127.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	709	938
1	2966	838
2	5002	830

prune250.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 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))

rewrite84.0ms

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:

18.0ms	(* (* 2.0 PI) n)
17.0ms	(* (* 2.0 PI) n)
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
23.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series309.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (* 2.0 PI) n)
28.0ms	(* (* 2.0 PI) n)
127.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
125.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	399	798
1	1625	738
2	5001	694

prune391.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 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))

rewrite85.0ms

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:

19.0ms	(* (* 2.0 PI) n)
17.0ms	(* (* 2.0 PI) n)
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
23.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series310.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) n)
28.0ms	(* (* 2.0 PI) n)
126.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
124.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	399	798
1	1625	738
2	5001	694

prune353.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes111.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	19
1	18	19

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.0s	20243×	body	80	nan
742.0ms	11967×	body	80	valid
0.0ms	1×	body	160	nan