This is to show how to get shorter algorithms by searching for positions close to positions already existing in database.

The distance between two cube positions is expressed as the number of sticker locations that differ between the two positions.
This number should be divided by 3 for corners and by 2 for midges to get the distance in number of pieces, instead of number of stickers.
Two positions are considered close if they differ by only 1,2 or 3 permuted pieces.

Algorithms of positions that are not yet in database may be obtained from those of close positions already in database, as shown below.

Test case: Edge-Center Edge-Center Pair 2(3c) = (3c)&(3c)

Check 'Find nearest position' in Orbit Solver to query database
If 'distance' is '0', then the position already exists in database and the permutation is not factorized.
If 'distance' is  greater than '0', then the position doesn't yet exists in database and the permutation is factorized.

1- Using Orbit Solver, search for this cycle already in database: (MOX)&(JDU)

Orbit Solver gives:
Cube order: 7
Orbit number: 13
Permutation: (MOX)&(JDU)
Algorithm (12 moves) (18 QTM moves) (6 permuted stickers) (6 permuted pieces) (Orbit Parity: Even):
R' N3U2 NB2 N3U' NB2 NL2 N3U' R2 N3U NL2 N3U' R'

Nearest position algorithm at distance 0 (12 moves):
R' N3U2 NB2 N3U' NB2 NL2 N3U' R2 N3U NL2 N3U' R'

The distance being '0', this confirms that the position already exists in database.


2- Using Orbit Solver, search for this cycle not (yet) in database: (MOX)&(JDW)

Orbit Solver gives:
Cube order: 7
Orbit number: 13
Permutation: (MOX)&(JDW)
Algorithm (16 moves) (22 QTM moves) (6 permuted stickers) (6 permuted pieces) (Orbit Parity: Even):
N3D NL2 N3D' L2 N3D NL2 N3D' L2 F NU F' N3U2 F NU' F' N3U2

Nearest position algorithm at distance 1 (7 moves):
R' N3U2 NB2 N3U' NB2 N3U' R

The distance being '1', this indicates that the position doesn't already exists in database.


3- Using Algorithm Finder Lite:
- Copy (R' N3U2 NB2 N3U' NB2 N3U' R) to the 'Template(s)' window
- Copy (N3D NL2 N3D' L2 N3D NL2 N3D' L2 F NU F' N3U2 F NU' F' N3U2) to the 'Generator' window
- Check 'Shift template', 'Invert template', 'Apply rotation symmetry' and 'Apply reflection symmetry'
- Select 2 setup moves
- Launch AFL

AFL then gives:

Generator algorithm: N3D NL2 N3D' L2 N3D NL2 N3D' L2 F NU F' N3U2 F NU' F' N3U2

1 template(s):
X Y R' N3U2 NB2 N3U' NB2 N3U' R Y' X'

1 algorithm(s):
[0] NR' N3F R' N3U2 NB2 N3U' NB2 N3U' R N3F' NR (11 moves) (6 solved stickers) (Order: 3)

A gain of 5 moves has thus been obtained (from 16 down to 11).

This shows that the database could be improved by adding the newly found algorithm to the list of seeds (next version).