Details

sample78.0ms

Algorithm

intervals

Results

33.0ms	569×	body	80	nan
22.0ms	358×	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	1044	8
5	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

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

rewrite47.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 157

Calls

4 calls:

18.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(/ 1.0 (sqrt k))
7.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series574.0ms

Counts

4 → 12

Calls

4 calls:

346.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
40.0ms	(/ 1.0 (sqrt k))
40.0ms	(* (* 2.0 PI) n)
147.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify104.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5003	1383

prune489.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
24×	`sqrt-prod`
19×	`add-exp-log` `pow-unpow`
15×	`pow1`
13×	`add-cbrt-cube`
12×	`associate-/r*`
6×	`pow-prod-down` `prod-exp` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 140

Calls

4 calls:

3.0ms	(/ 1.0 (sqrt k))
3.0ms	(/ 1.0 (sqrt k))
11.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series273.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1.0 (sqrt k))
39.0ms	(/ 1.0 (sqrt k))
40.0ms	(* (* 2.0 PI) n)
147.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	579	912
1	2248	843
2	5001	807

prune499.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
133×	`add-sqr-sqrt` `*-un-lft-identity`
127×	`add-cube-cbrt`
84×	`sqrt-prod`
48×	`cbrt-prod`
19×	`pow-unpow`
15×	`add-exp-log`
13×	`associate-/l*`
12×	`div-inv`
10×	`pow1`
9×	`associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-pow` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`pow-to-exp` `unpow-prod-down` `frac-2neg` `div-sub` `clear-num` `associate-/l/` `pow-sub` `sqr-pow`

Counts

4 → 220

Calls

4 calls:

13.0ms	(/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))
0.0ms	(cbrt k)
1.0ms	(cbrt k)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series810.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))
185.0ms	(cbrt k)
192.0ms	(cbrt k)
148.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	929	2689
1	3525	2585
2	5001	2527

prune983.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
38×	`pow-unpow`
34×	`sqrt-prod`
31×	`add-cube-cbrt`
30×	`times-frac`
28×	`pow1`
23×	`add-exp-log`
12×	`pow-prod-down` `sqr-pow`
11×	`associate-r` `add-cbrt-cube`
10×	`swap-sqr` `prod-exp`
9×	`associate-l` `unswap-sqr`
6×	`unpow-prod-down` `pow-pow` `sqrt-pow1` `pow1/2` `div-sub` `pow-exp` `distribute-lft-out--` `pow-sub` `difference-of-squares`
4×	`expm1-log1p-u` `sqrt-div` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr` `pow-prod-up`
2×	`pow-to-exp` `*-commutative` `div-inv`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `rem-square-sqrt`

Counts

4 → 159

Calls

4 calls:

7.0ms	(* (* 2.0 PI) n)
16.0ms	(* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series666.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* 2.0 PI) n)
146.0ms	(* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
332.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
151.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	503	1504
1	2269	1388
2	5001	1344

prune526.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes109.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	21
1	21	21

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	20780×	body	80	nan
725.0ms	11983×	body	80	valid
0.0ms	2×	body	160	nan