Details

sample141.0ms

Algorithm

intervals

Results

53.0ms	931×	body	80	nan
20.0ms	350×	body	80	valid
17.0ms	49×	body	1280	nan
13.0ms	49×	body	640	nan
6.0ms	31×	body	320	nan
2.0ms	14×	body	160	nan

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: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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:

9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))

series544.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
324.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(* (* 2.0 PI) n)
37.0ms	(/ 1.0 (sqrt k))

simplify99.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	950	1461
1	3925	1358
2	5003	1344

prune419.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
105×	`prod-exp`
39×	`pow-exp`
36×	`div-exp`
26×	`add-cbrt-cube`
20×	`pow1`
13×	`add-sqr-sqrt` `pow-to-exp` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
10×	`times-frac` `cbrt-unprod`
9×	`pow-prod-down`
6×	`associate-r`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-pow`
2×	`associate-l` `*-commutative` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/r` `associate-/l` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
10.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

260.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
891.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
31.0ms	(* (* 2.0 PI) n)
37.0ms	(* (* 2.0 PI) n)

simplify242.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	916	1358
1	3952	1199
2	5002	1199

prune278.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

222×	`add-exp-log`
140×	`prod-exp`
45×	`pow-exp`
42×	`div-exp`
35×	`add-cbrt-cube`
23×	`pow1`
16×	`cbrt-unprod`
15×	`associate-r`
13×	`pow-to-exp`
12×	`pow-prod-down`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
4×	`cbrt-undiv` `add-log-exp`
3×	`associate-l` `*-commutative`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 122

Calls

4 calls:

11.0ms	(/ (* 1.0 (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms	(* (* 2.0 PI) n)
6.0ms	(* (* 2.0 PI) (sqrt n))
10.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

series1.1s

Counts

4 → 12

Calls

4 calls:

961.0ms	(/ (* 1.0 (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
31.0ms	(* (* 2.0 PI) n)
75.0ms	(* (* 2.0 PI) (sqrt n))
51.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

simplify115.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	1001	1626
1	4507	1411
2	5001	1315

prune284.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (* 2.0 PI) n) (* 2 (/ (/ 1.0 2.0) 2)))
0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)
0.3b	(/ (pow (* (* 2.0 PI) n) (* 2 (/ (/ 1.0 2.0) 2))) (/ (sqrt k) 1.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
107×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
49×	`add-exp-log`
24×	`unpow-prod-down` `sqr-pow`
22×	`associate-/r*`
20×	`pow1`
19×	`add-cbrt-cube`
15×	`div-exp` `prod-exp`
9×	`pow-prod-down` `pow-exp`
7×	`div-inv`
6×	`associate-r` `cbrt-unprod`
5×	`associate-/l*`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-pow`
2×	`associate-l` `*-commutative`
1×	`pow-unpow` `frac-2neg` `clear-num` `associate-/r/`

Counts

4 → 213

Calls

4 calls:

5.0ms	(pow (* (* 2.0 PI) n) (* 2 (/ (/ 1.0 2.0) 2)))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
12.0ms	(/ (pow (* (* 2.0 PI) n) (* 2 (/ (/ 1.0 2.0) 2))) (/ (sqrt k) 1.0))

series891.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(pow (* (* 2.0 PI) n) (* 2 (/ (/ 1.0 2.0) 2)))
38.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)
560.0ms	(/ (pow (* (* 2.0 PI) n) (* 2 (/ (/ 1.0 2.0) 2))) (/ (sqrt k) 1.0))

simplify116.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	946	3323
1	4305	3173
2	5003	3173

prune629.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes120.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	26963×	body	80	nan
673.0ms	1925×	body	1280	nan
643.0ms	10669×	body	80	valid
464.0ms	1708×	body	640	nan
147.0ms	794×	body	320	nan
44.0ms	392×	body	160	nan