Extensions allow the engine to look deeper into interesting combinations, thus slowing down the search.
The UCI option "extend" gives you six choices what to extend:
if set to 0, no moves are extended
if set to 1, forced moves are extended (formerly "extend force"), strongly recommended
if set to 2, also checking moves are extended (formerly "extend check")
if set to 3, also recaptures of sacrifices in favoured lines are extended ("extend gambit" in version 0.4.5.2)
if set to 4, also arbitrary evasions of dangerous checks are extended in favoured lines (stronger "extend gambit" in version 0.4.6)
if set to 5, also preferred replies to arbitrary checks are extended in favoured lines (new in 0.4.6.1)
Reductions allow the engine to reduce the search effort for unlikely continuations.
Setting the option "reduce" to 1 activates nullmove pruning,
i.e. skipping the analysis of positions that appear to be strong even if the strong side waives its right to move.
The maximum setting of 2 also activates reduction of moves that are tested after an acceptable continuation of a line has been found.
This is a rather blunt implementation of Late Move Reductions by Tord Romstad,
author of the great Open Source engine Glaurung .
Recommendations
The default options (reduce 2, extend 2) are optimised for gameplay.
For the analyis of sharp positions and mate problems, it may be useful to raise the level of extensions to 3, 4 or 5.
To obtain a more precise analysis, it is recommended to lower the level of reduction to 1.
If you want to be certain that the best move is found, you should disable all reductions.
