fier">x</span><span class="special">);</span>
</pre>
<p>
      Finite differencing is complicated, as finite-difference approximations to
      the derivative are <span class="emphasis"><em>infinitely</em></span> ill-conditioned. In addition,
      for any function implemented in finite-precision arithmetic, the "true"
      derivative is <span class="emphasis"><em>zero</em></span> almost everywhere, and undefined at
      representables. However, some tricks allow for reasonable results to be obtained
    