Check the environment variables set by your web server. The Alexa toolbar changes the browser version string. An example : "Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1; Alexa Toolbar)"

if ($ENV{HTTP_USER_AGENT} =~ /Alexa/) { print "$ENV{HTTP_USER_AGENT}"; }

The %ENV hash holds all the environment variables. The Apache web server (and I assume others) set the HTTP_USER_AGENT string equal to what the web browser sends, so that you can detect what version of Internet Explorer, Netscape Navigator, or Mozilla Firefox someone is running. In this case, Alexa also changes this string to include itself.