evaluation of the derivative. It also expands
      the domain over which the function must be differentiable and requires the
      function to have two more continuous derivatives. The error estimate is computed
      under the assumption that <span class="emphasis"><em>f</em></span> is evaluated to 1ULP. This
      might seem an extreme assumption, but it is the only sensible one, as the routine
      cannot know the functions rounding error. If the function cannot be evaluated
      with very great accu