Then the example given, modified to affect STDERR.....

open( STDERR, ">errors.log") or die "Cannot open error log.\n$!";
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The tutorial also suggests that that it can be a clever thing to do to close the STD... filehandle on exit from the program, to force a flush.

END { close STDERR or die "Can't close STDERR.\n$!" }
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In your case, you simply want to redirect STDERR to the OUTFILE file handle. Also listed in the tutorial, you may do this:

open (STDERR, ">>&OUTFILE") or die "Can't redirect STDERR.\n$!";
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Hope this helps!