Details

sample219.0ms

Algorithm

intervals

Results

87.0ms	983×	body	80	nan
38.0ms	346×	body	80	valid
32.0ms	69×	body	1280	nan
20.0ms	54×	body	640	nan
6.0ms	23×	body	320	nan
1.0ms	10×	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	1044	8
5	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

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	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite41.0ms

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:

17.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series555.0ms

Counts

4 → 12

Calls

4 calls:

331.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
45.0ms	(/ 1.0 (sqrt k))
32.0ms	(* (* 2.0 PI) n)
146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (88.0ms)

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

prune469.0ms

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

rewrite33.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `div-inv` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

7.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
6.0ms	(* (* 2.0 PI) n)
7.0ms	(* (* 2.0 PI) n)
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series457.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
38.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)
264.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	463	557
1	1809	510
2	5001	503

prune332.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow n (/ (- 1.0 k) 2.0))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.6b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
70×	`times-frac`
64×	`*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
23×	`sqrt-prod`
22×	`associate-l`
11×	`prod-exp` `add-cbrt-cube`
8×	`pow1`
7×	`pow-exp`
6×	`associate-/r*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`
5×	`unpow-prod-down` `div-exp` `associate-r`
4×	`expm1-log1p-u` `pow-to-exp` `div-sub` `log1p-expm1-u` `div-inv` `pow-sub` `add-log-exp`
3×	`pow-pow` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 169

Calls

4 calls:

8.0ms	(pow n (/ (- 1.0 k) 2.0))
3.0ms	(/ 1.0 (sqrt k))
15.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
5.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series472.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow n (/ (- 1.0 k) 2.0))
46.0ms	(/ 1.0 (sqrt k))
287.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
81.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	844	1367
1	3255	1284
2	5002	1267

prune552.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize24.0ms

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

356×	`add-exp-log`
201×	`prod-exp`
126×	`div-exp`
104×	`times-frac`
100×	`pow-exp`
90×	`add-sqr-sqrt`
77×	`pow-to-exp` `*-un-lft-identity`
71×	`add-cube-cbrt`
58×	`associate-r`
44×	`unpow-prod-down`
32×	`add-cbrt-cube`
23×	`associate-l` `sqrt-prod`
19×	`pow-unpow` `sqr-pow`
12×	`cbrt-unprod`
9×	`pow1`
7×	`cbrt-undiv` `div-sub` `pow-sub`
6×	`frac-times` `associate-l/` `associate-/r` `unswap-sqr`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`pow-pow` `pow-prod-down` `*-commutative`
1×	`frac-2neg` `clear-num`

Counts

4 → 301

Calls

4 calls:

42.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (pow n (/ 1.0 2.0)) (pow n (/ k 2.0))))
3.0ms	(/ 1.0 (sqrt k))
15.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
6.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

792.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (pow n (/ 1.0 2.0)) (pow n (/ k 2.0))))
39.0ms	(/ 1.0 (sqrt k))
298.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
79.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

313 → 313

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1694	3820
1	5002	3512

prune793.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes140.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	16
1	22	16

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.3s	26987×	body	80	nan
1.2s	10603×	body	80	valid
1.2s	1974×	body	1280	nan
630.0ms	1683×	body	640	nan
221.0ms	858×	body	320	nan
54.0ms	368×	body	160	nan
6.0ms	4×	body	10240	exit