Details

sample148.0ms

Algorithm

intervals

Results

52.0ms	874×	body	80	nan
22.0ms	62×	body	1280	nan
21.0ms	344×	body	80	valid
17.0ms	65×	body	640	nan
3.0ms	17×	body	320	nan
2.0ms	15×	body	160	nan

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

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

rewrite176.0ms

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:

152.0ms	(* (/ 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))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series549.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
33.0ms	(* (* 2.0 PI) n)
42.0ms	(/ 1.0 (sqrt k))
144.0ms	(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

prune463.0ms

Filtered

169 candidates to 119 candidates (70.4%)

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

rewrite31.0ms

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:

5.0ms	(* (* 2.0 PI) n)
6.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series462.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* 2.0 PI) n)
39.0ms	(* (* 2.0 PI) n)
126.0ms	(pow (* (* 2.0 PI) n) (/ k 2.0))
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

prune339.0ms

Filtered

114 candidates to 75 candidates (65.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

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 k) 2.0))))
0.3b	(/ 1.0 (sqrt k))
0.4b	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.7b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log`
72×	`prod-exp`
57×	`add-sqr-sqrt`
51×	`times-frac`
50×	`*-un-lft-identity`
44×	`add-cube-cbrt`
32×	`pow-exp`
27×	`associate-l`
22×	`pow-to-exp`
21×	`sqrt-prod`
20×	`add-cbrt-cube`
19×	`pow-unpow`
14×	`div-exp`
13×	`div-sub` `pow-sub`
9×	`pow1`
8×	`associate-r` `sqr-pow`
7×	`unpow-prod-down` `cbrt-unprod`
6×	`frac-times` `associate-r/` `associate-/r` `unswap-sqr`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-prod-down` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`pow-pow` `*-commutative`
1×	`frac-2neg` `clear-num`

Counts

4 → 193

Calls

4 calls:

13.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
8.0ms	(/ 1.0 (sqrt k))
8.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
7.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

608.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
40.0ms	(/ 1.0 (sqrt k))
297.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
82.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify121.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1124	2196
1	4652	1983
2	5001	1979

prune562.0ms

Filtered

205 candidates to 130 candidates (63.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.3b	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
0.3b	(/ 1.0 (sqrt k))
0.7b	(pow PI (/ (- 1.0 k) 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
66×	`prod-exp`
53×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
35×	`pow-to-exp` `add-cube-cbrt` `pow-exp`
33×	`times-frac`
19×	`pow-unpow`
18×	`unpow-prod-down`
17×	`div-sub` `pow-sub`
14×	`associate-l`
13×	`add-cbrt-cube`
12×	`sqrt-prod`
10×	`sqr-pow`
9×	`unswap-sqr`
8×	`associate-r`
6×	`frac-times` `associate-r/` `associate-/r`
5×	`pow1`
4×	`expm1-log1p-u` `associate-*l/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative` `div-inv`
1×	`cbrt-undiv` `pow-pow` `frac-2neg` `div-exp` `clear-num`

Counts

4 → 182

Calls

4 calls:

8.0ms	(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
11.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
5.0ms	(/ 1.0 (sqrt k))
6.0ms	(pow PI (/ (- 1.0 k) 2.0))

series727.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
434.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
40.0ms	(/ 1.0 (sqrt k))
55.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify111.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	1027	1856
1	4227	1618
2	5001	1613

prune571.0ms

Filtered

194 candidates to 125 candidates (64.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes151.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	14
1	18	14

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.6s	27259×	body	80	nan
695.0ms	1911×	body	1280	nan
654.0ms	10672×	body	80	valid
451.0ms	1691×	body	640	nan
155.0ms	808×	body	320	nan
49.0ms	422×	body	160	nan