Is it possible to reduce the duplication in this simple query?
Two levels of derived tables (subquery or CTE) to avoid all repeated calculations:
SELECT a, b, c
FROM  (
   SELECT z, a, b, a / b AS c
   FROM (
      SELECT z
           , x + y AS a
           , x + z AS b
      FROM   integers
      ) i
   ) i
ORDER  BY  z + c DESC
LIMIT  10;

With simple expressions, it won't matter for performance.
What might matter with repeating more expensive expressions is that all involved functions have (correct!) volatility STABLE or IMMUTABLE. See:

Can declaring function volatility IMMUTABLE harm performance?