You don't show how you're actually using Compress::Zlib, which might be relevant. If you are reading uncompressed data from some source, passing it to a Zlib method and writing the result to a file, maybe it would be sufficient to keep count of the input data (e.g.  $read_count += length()), and then compare this to the finished size of the output compressed file -- e.g.

...
close OUTZ;

my $comp_count = (-s $outzfile);

printf("Input byte count: %d; output byte count: %d; ratio: %3.1f\n",
        $read_count, comp_count, 100*$comp_count/$read_count );

# (updated: reporting "100*$read_count/$comp_count would not be right)
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Adding a time stamp to that is trivial (see scalar localtime).