Only the shell knows about elements on the command line beyond any re-direction, so in the command line invocation

file.pl update directoryname/error.txt directoryname/filename.txt >& d
+irectoryname/filename.log
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, directoryname/filename.log is not (directly) accessible to the script.

Given that your script knows its own PID ($$), you may be able to parse it [the full command line] from the process tree e.g. by parsing the output from ps -fp $$...