Pipe STDERR with 2>&1, see https://stackoverflow.com/questions/818255/in-the-shell-what-does-21-mean

script.sh

# Standard error is redirected to standard output, so both are redirected to debug.log
perl test.pl > debug.log 2>&1

# Standard output goes to out.log, and standard error to err.log
perl test.pl 1>out.log 2>err.log