Details

sample205.0ms

Algorithm

intervals

Results

72.0ms	752×	body	80	nan
34.0ms	62×	body	1280	nan
32.0ms	329×	body	80	valid
25.0ms	60×	body	640	nan
9.0ms	32×	body	320	nan
2.0ms	12×	body	160	nan

simplify36.0ms

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: 0.5b

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

rewrite46.0ms

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:

18.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
10.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms	(/ 1.0 (sqrt k))

series531.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
30.0ms	(* (* 2.0 PI) n)
142.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
38.0ms	(/ 1.0 (sqrt k))

simplify97.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (81.0ms)

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

prune437.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(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))))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)

rewrite37.0ms

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:

7.0ms	(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))))
7.0ms	(* (* 2.0 PI) n)
7.0ms	(* (* 2.0 PI) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

266.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
884.0ms	(/ (* 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)
36.0ms	(* (* 2.0 PI) n)

simplify98.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (19.0ms)

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

prune292.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

236×	`add-exp-log`
118×	`prod-exp`
85×	`add-sqr-sqrt`
83×	`times-frac`
77×	`div-exp`
60×	`pow-exp`
45×	`add-cube-cbrt` `*-un-lft-identity`
35×	`associate-r`
28×	`add-cbrt-cube`
26×	`sqrt-prod`
24×	`associate-l`
22×	`sqr-pow`
20×	`pow-to-exp`
16×	`pow1`
15×	`unswap-sqr`
10×	`unpow-prod-down` `cbrt-unprod`
7×	`pow-prod-down`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 209

Calls

4 calls:

32.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
7.0ms	(* (* 2.0 PI) n)
7.0ms	(* (* 2.0 PI) n)
3.0ms	(/ 1.0 (sqrt k))

series865.0ms

Counts

4 → 12

Calls

4 calls:

759.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
37.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)
38.0ms	(/ 1.0 (sqrt k))

simplify58.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1271	2638
1	5001	2478

prune579.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize22.0ms

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))))
0.3b	(* (* 2.0 PI) n)
0.4b	(* (* 2.0 PI) (sqrt n))
0.4b	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

rewrite60.0ms

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:

13.0ms	(/ (* 1.0 (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
6.0ms	(* (* 2.0 PI) n)
8.0ms	(* (* 2.0 PI) (sqrt n))
26.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

series1.1s

Counts

4 → 12

Calls

4 calls:

952.0ms	(/ (* 1.0 (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
30.0ms	(* (* 2.0 PI) n)
76.0ms	(* (* 2.0 PI) (sqrt n))
49.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

simplify110.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (96.0ms)

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

prune386.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes152.0ms

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	24	15
1	24	15

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.4s	26647×	body	80	nan
1.1s	10653×	body	80	valid
1.1s	1935×	body	1280	nan
694.0ms	1636×	body	640	nan
243.0ms	773×	body	320	nan
79.0ms	429×	body	160	nan