Details

sample143.0ms

Algorithm

intervals

Results

47.0ms	874×	body	80	nan
23.0ms	344×	body	80	valid
21.0ms	62×	body	1280	nan
16.0ms	65×	body	640	nan
3.0ms	17×	body	320	nan
2.0ms	15×	body	160	nan

simplify38.0ms

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: 0.6b

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	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite39.0ms

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:

11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(/ 1.0 (sqrt k))
12.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series523.0ms

Counts

4 → 12

Calls

4 calls:

315.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
41.0ms	(/ 1.0 (sqrt k))
136.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify98.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (83.0ms)

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

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)
0.2b	(pow (* (* 2.0 PI) n) (/ k 2.0))
0.4b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1` `add-exp-log` `pow-unpow`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
6×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod`
4×	`add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `div-inv` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
6.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series448.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)
124.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
254.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	453	528
1	1774	479
2	5002	473

prune308.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
0.3b	(/ 1.0 (sqrt k))
0.4b	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.7b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log`
72×	`prod-exp`
57×	`add-sqr-sqrt`
51×	`times-frac`
50×	`*-un-lft-identity`
44×	`add-cube-cbrt`
32×	`pow-exp`
27×	`associate-l`
22×	`pow-to-exp`
21×	`sqrt-prod`
20×	`add-cbrt-cube`
19×	`pow-unpow`
14×	`div-exp`
13×	`div-sub` `pow-sub`
9×	`pow1`
8×	`associate-r` `sqr-pow`
7×	`unpow-prod-down` `cbrt-unprod`
6×	`frac-times` `associate-r/` `associate-/r` `unswap-sqr`
4×	`associate-*l/` `add-log-exp`
3×	`cbrt-undiv` `pow-prod-down` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`pow-pow` `*-commutative`
1×	`frac-2neg` `clear-num`

Counts

4 → 185

Calls

4 calls:

16.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
4.0ms	(/ 1.0 (sqrt k))
7.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
7.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series979.0ms

Counts

4 → 12

Calls

4 calls:

580.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
37.0ms	(/ 1.0 (sqrt k))
282.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
79.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify124.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	1088	2140
1	4536	1954
2	5001	1947

prune526.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.3b	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
0.3b	(/ 1.0 (sqrt k))
0.7b	(pow PI (/ (- 1.0 k) 2.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 174

Calls

4 calls:

8.0ms	(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
10.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
4.0ms	(/ 1.0 (sqrt k))
6.0ms	(pow PI (/ (- 1.0 k) 2.0))

series682.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
407.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
37.0ms	(/ 1.0 (sqrt k))
50.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify110.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	995	1807
1	4090	1569
2	5002	1555

prune524.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes152.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	14
1	18	14

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	27259×	body	80	nan
668.0ms	1911×	body	1280	nan
657.0ms	10672×	body	80	valid
443.0ms	1691×	body	640	nan
154.0ms	808×	body	320	nan
47.0ms	422×	body	160	nan