Source : Free On-Line Dictionary of Computing

strength reduction
     
        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        Here the expensive operation (2**x) has been replaced by the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'.
     
        (1995-01-31)