s
      <span class="emphasis"><em>C</em></span> &#949;<sup>k/k+1</sup>. In the limit <span class="emphasis"><em>k</em></span> &#8594;
      &#8734;, we see that the error tends to &#949;, recovering the full precision
      for the type. However, this ignores the fact that higher-order methods require
      subtracting more nearly-equal (perhaps noisy) terms, so the constant <span class="emphasis"><em>C</em></span>
      grows with <span class="emphasis"><em>k</em></span>. Since <span class="emphasis"><em>