Details

sample94.0ms

Algorithm

intervals

Results

39.0ms	650×	body	80	nan
24.0ms	372×	body	80	valid

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: 0.3b

localize14.0ms

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	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite91.0ms

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:

38.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
20.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series526.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(* (* 2.0 PI) n)
35.0ms	(/ 1.0 (sqrt k))
140.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (85.0ms)

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

prune465.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
157×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
122×	`pow-unpow`
117×	`add-cube-cbrt`
88×	`add-exp-log`
61×	`prod-exp`
36×	`pow-exp`
18×	`distribute-lft-out--` `difference-of-squares`
16×	`pow1`
12×	`pow-to-exp` `div-sub` `sqrt-prod`
10×	`sqr-pow`
9×	`div-inv`
8×	`add-cbrt-cube`
7×	`pow-prod-down`
6×	`unpow-prod-down` `pow-pow` `associate-/r*` `pow-sub`
5×	`swap-sqr` `associate-r` `associate-l`
4×	`add-log-exp` `unswap-sqr`
3×	`associate-/l*`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `associate-r/` `div-exp` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 255

Calls

4 calls:

43.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
6.0ms	(/ 1.0 (sqrt k))
28.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
26.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series503.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
36.0ms	(/ 1.0 (sqrt k))
140.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
138.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify102.0ms

Algorithm

egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	971	2554
1	3864	2347
2	5001	2312

prune861.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(pow (pow (* (* 2.0 PI) n) (* 0.25 (- 1.0 k))) 2)
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (* 0.25 (- 1.0 k)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`pow1`
12×	`sqrt-prod`
11×	`unpow-prod-down` `pow-exp` `add-cbrt-cube`
9×	`prod-exp`
8×	`unpow-prod-up`
6×	`pow-prod-down` `associate-/r*`
4×	`distribute-rgt-in` `sub-neg` `pow-unpow` `pow-pow` `distribute-lft-in` `add-log-exp`
3×	`pow-to-exp` `associate-r` `cbrt-unprod` `associate-/l*` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative` `div-inv` `unpow2`

Counts

4 → 106

Calls

4 calls:

17.0ms	(* (* 2.0 PI) n)
12.0ms	(pow (pow (* (* 2.0 PI) n) (* 0.25 (- 1.0 k))) 2)
9.0ms	(/ 1.0 (sqrt k))
18.0ms	(pow (* (* 2.0 PI) n) (* 0.25 (- 1.0 k)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
188.0ms	(pow (pow (* (* 2.0 PI) n) (* 0.25 (- 1.0 k))) 2)
35.0ms	(/ 1.0 (sqrt k))
140.0ms	(pow (* (* 2.0 PI) n) (* 0.25 (- 1.0 k)))

simplify72.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	648	877
1	2676	795
2	5001	784

prune340.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.6b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

17.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
24.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series346.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
42.0ms	(/ 1.0 (sqrt k))
133.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
140.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify61.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	563	968
1	2197	904
2	5001	886

prune459.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes377.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	13
1	19	13

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	20324×	body	80	nan
758.0ms	11719×	body	80	valid
0.0ms	1×	body	160	nan