Put the main slash in the script name, i.e.
/usr/bin/php /home/domain.com/public_html/cron/script.php
If you are not really going to run the script over the Internet, as in response to lacqui, and you do not mind random third parties who can run it at any time convenient for them, there is no reason why you should put it in your public_html catalog; quite the opposite.
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