Another way would be to install die() and warn() handlers in %SIG to log to a file. Localise them to just the bit of code that you're interested in:

local $SIG{__DIE__} = sub {
    open LOGFILE, '>>logfile'; print LOGFILE 'die: ', @_;
    die("Died, errors logged to file\n");
}
local $SIG{__WARN__} = sub {
    open LOGFILE, '>>logfile'; print LOGFILE 'warn: ', @_;
    close LOGFILE;
}
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It may also be useful to log a timestamp for all die()s and warn()s, and spit out stack traces.