How can we discover the machine name of $conf keys?
By literally looking at the DOM.

For a random example, take the aggregate CSS checkbox on the Performance page:

&lt;div class="form-item form-type-checkbox form-item-preprocess-css"&gt;
 &lt;input type="checkbox" id="edit-preprocess-css" name="preprocess_css" value="1" class="form-checkbox"&gt;  
 &lt;label class="option" for="edit-preprocess-css"&gt;Aggregate and compress CSS files. &lt;/label&gt;
&lt;/div&gt;


You'll find the machine name for the variable in the name attribute of the associated &lt;input&gt; element. In this case, preprocess_css.