An optimisation where a function of some systematically
changing variable is calculated more efficiently by using
previous values of the function. In a procedural language
this would apply to an expression involving a loop variable
and in a declarative language it would apply to the argument
of a recursive function. E.g.

f x = ... (2**x) ... (f (x+1)) ...
==>
f x = f' x (2**x)
where
f ' x z = ... z ... (f' (x+1) 2*z) ...

Here the expensive operation (2**x) has been replaced by the
cheaper 2*z in the recursive function f'. This maintains the
invariant that z = 2**x for any call to f'.