Depending on the quantity of the logging information you're expecting to produce, it might be worth using the standard logger tool to write it to the user syslog in /var/log:

/path/to/myprog 2>&1 | logger -p user.debug -t 'myprog'

Here is an example of the output written to /var/log/debug on my Debian-based system:

Jul 31 00:17:09 myserver myprog: test message with user.debug

There are various facility/level pairs available for use. You might want to consider user.notice or user.info or user.debug. Just be aware that some of these may also get written to /var/log/messages and /var/log/syslog.

Depending on the quantity of the logging information you're expecting to produce, it might be worth using the standard logger tool to write it to the user syslog in /var/log:

1 */8 * * * /path/to/myprog 2>&1 | logger -p user.debug -t 'myprog'

Here is an example of the output written to /var/log/debug on my Debian-based system:

Jul 31 00:17:09 myserver myprog: test message with user.debug

There are various facility/level pairs available for use. You might want to consider user.notice or user.info or user.debug. Just be aware that some of these may also get written to /var/log/messages and /var/log/syslog.

If you want to differentiate stdout and stderr in your cron job, sending only stderr to the logger, you can use a construct like this, which I'm sure others will improve upon:

1 */8 * * * ( /path/to/myprog 2>&1 1>&3 | logger -p user.debug -t 'myprog' ) 3>&1