I've found a few questions which answer the question of saddle height changes in relation to a change in crank length, however I haven't found any questions relating to compensatory changes in fore-aft when crank length is changed.
If one changes their crank length from, say, 175mm to 165mm, then their saddle height should (in theory) move up approximately 10mm to compensate (when measured from the bottom bracket centre; the height from the pedal at full extension would therefore stay the same as it was before).
What does one do to saddle fore-aft to appropriately compensate for the crank length change, if anything?
EDIT: Just to expand upon/clarify what I am looking to evaluate; there will of course be a change in the effective setback which comes as a result of saddle height changes, which can be calculated using trigonometry.
However, the intention of my question was more to clarify whether a change in setback would be appropriate due to the change in effective forward "reach" of the leg at the front (3 o'clock) position of the crank given it is hypothetically now 10mm shorter. Likewise the rear (9 o'clock) position is 10mm further forward than it was.
To take the saddle height part of a crank length change once more; as a general rule of thumb, you change the saddle -> BB center measurement by the same amount that the crank length has changed (10mm shorter cranks = 10mm higher saddle relative to the BB center, with a tiny adjustment for relative setback if you wish).
Is there a similar rule of thumb for setback given the same crank length change?
The answer may be that no change is necessary/appropriate but reasoning would be appreciated!