John Hughes's optimisation of lambda lifting to give full
laziness. Maximal free expressions are shared to minimise
the amount of recalculation. Each inner sub-expression is
replaced by a function of its maximal free expressions
(expressions not containing any bound variable) applied to
those expressions. E.g.

f = \ x . (\ y . (+) (sqrt x) y)

((+) (sqrt x)) is a maximal free expression in
(\ y . (+) (sqrt x) y) so this inner abstraction is replaced
with

(\ g . \ y . g y) ((+) (sqrt x))

Now, if a partial application of f is shared, the result of
evaluating (sqrt x) will also be shared rather than
re-evaluated on each application of f. As Chin notes, the
same benefit could be achieved without introducing the new
higher-order function, g, if we just extracted out (sqrt x).

This is similar to the code motion optimisation in
procedural languages where constant expressions are moved
outside a loop or procedure.