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    <h1>criterion performance measurements</h1>

<h2>overview</h2>

<p><a href="#grokularation">want to understand this report?</a></p>

<div id="overview" class="ovchart" style="width:900px;height:100px;"></div>

{{#report}}
<h2><a name="b{{number}}">{{name}}</a></h2>
 <table width="100%">
  <tbody>
   <tr>
    <td><div id="kde{{number}}" class="kdechart"
             style="width:450px;height:278px;"></div></td>
    <td><div id="time{{number}}" class="timechart"
             style="width:450px;height:278px;"></div></td>
<!--
    <td><div id="cycle{{number}}" class="cyclechart"
             style="width:300px;height:278px;"></div></td>
-->
   </tr>
  </tbody>
 </table>

 <table>
  <thead class="analysis">
   <th></th>
   <th class="cibound"
       title="{{anMean.estConfidenceLevel}} confidence level">lower bound</th>
   <th>estimate</th>
   <th class="cibound"
       title="{{anMean.estConfidenceLevel}} confidence level">upper bound</th>
  </thead>
  <tbody>
   <tr>
    <td>OLS regression</td>
    <td><span class="confinterval olstimelb{{number}}">xxx</span></td>
    <td><span class="olstimept{{number}}">xxx</span></td>
    <td><span class="confinterval olstimeub{{number}}">xxx</span></td>
   </tr>
   <tr>
    <td>R&#xb2; goodness-of-fit</td>
    <td><span class="confinterval olsr2lb{{number}}">xxx</span></td>
    <td><span class="olsr2pt{{number}}">xxx</span></td>
    <td><span class="confinterval olsr2ub{{number}}">xxx</span></td>
   </tr>
   <tr>
    <td>Mean execution time</td>
    <td><span class="confinterval citime">{{anMean.estLowerBound}}</span></td>
    <td><span class="time">{{anMean.estPoint}}</span></td>
    <td><span class="confinterval citime">{{anMean.estUpperBound}}</span></td>
   </tr>
   <tr>
    <td>Standard deviation</td>
    <td><span class="confinterval citime">{{anStdDev.estLowerBound}}</span></td>
    <td><span class="time">{{anStdDev.estPoint}}</span></td>
    <td><span class="confinterval citime">{{anStdDev.estUpperBound}}</span></td>
   </tr>
  </tbody>
 </table>

 <span class="outliers">
   <p>Outlying measurements have {{anOutlierVar.ovDesc}}
     (<span class="percent">{{anOutlierVar.ovFraction}}</span>%)
     effect on estimated standard deviation.</p>
 </span>
{{/report}}

 <h2><a name="grokularation">understanding this report</a></h2>

 <p>In this report, each function benchmarked by criterion is assigned
   a section of its own.  The charts in each section are active; if
   you hover your mouse over data points and annotations, you will see
   more details.</p>

 <ul>
   <li>The chart on the left is a
     <a href="http://en.wikipedia.org/wiki/Kernel_density_estimation">kernel
       density estimate</a> (also known as a KDE) of time
     measurements.  This graphs the probability of any given time
     measurement occurring.  A spike indicates that a measurement of a
     particular time occurred; its height indicates how often that
     measurement was repeated.</li>

   <li>The chart on the right is the raw data from which the kernel
     density estimate is built.  The <i>x</i> axis indicates the
     number of loop iterations, while the <i>y</i> axis shows measured
     execution time for the given number of loop iterations.  The
     line behind the values is the linear regression prediction of
     execution time for a given number of iterations. Ideally, all
     measurements will be on (or very near) this line.</li>
 </ul>

 <p>Under the charts is a small table.
   The first two rows are the results of a linear regression run
     on the measurements displayed in the right-hand chart.</p>

 <ul>
   <li><i>OLS regression</i> indicates the
     time estimated for a single loop iteration using an ordinary
     least-squares regression model.  This number is more accurate
     than the <i>mean</i> estimate below it, as it more effectively
     eliminates measurement overhead and other constant factors.</li>
   <li><i>R&#xb2; goodness-of-fit</i> is a measure of how
     accurately the linear regression model fits the observed
     measurements.  If the measurements are not too noisy, R&#xb2;
     should lie between 0.99 and 1, indicating an excellent fit. If
     the number is below 0.99, something is confounding the accuracy
     of the linear model.</li>
   <li><i>Mean execution time</i> and <i>standard deviation</i> are
     statistics calculated from execution time
     divided by number of iterations.</li>
 </ul>

 <p>We use a statistical technique called
   the <a href="http://en.wikipedia.org/wiki/Bootstrapping_(statistics)">bootstrap</a>
   to provide confidence intervals on our estimates.  The
   bootstrap-derived upper and lower bounds on estimates let you see
   how accurate we believe those estimates to be.  (Hover the mouse
   over the table headers to see the confidence levels.)</p>

 <p>A noisy benchmarking environment can cause some or many
   measurements to fall far from the mean.  These outlying
   measurements can have a significant inflationary effect on the
   estimate of the standard deviation.  We calculate and display an
   estimate of the extent to which the standard deviation has been
   inflated by outliers.</p>

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   </div>
  </div>
  <div id="footer">
    <div class="body">
     <div class="footfirst">
      <h2>colophon</h2>
      <p>This report was created using the
	<a href="http://hackage.haskell.org/package/criterion">criterion</a>
	benchmark execution and performance analysis tool.</p>
      <p>Criterion is developed and maintained
      by <a href="http://www.serpentine.com/blog/">Bryan O'Sullivan</a>.</p>
     </div>
    </div>
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