CGI::Carp provides this functionality for you.

BEGIN {
    use CGI::Carp qw(carpout);
    open(LOG, ">>/usr/local/cgi-logs/mycgi-log") or
      die("Unable to open mycgi-log: $!\n");
    carpout(LOG);
}
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BTW, in case you are doing this to see error messages in the browser window, you should use:

use CGI::Carp qw(fatalsToBrowser);
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near the top of your CGI script.

Russ