The phrase "at infrequent intervals" means something that doesn't happen frequently or does so irregularly. There are several synonyms for this phrase that can be used interchangeably. One such synonym is "sporadically," which means something that occurs irregularly or in bursts. Another synonym is "intermittently," which means something that happens from time to time, but not consistently. An appropriate synonym is "occasionally," which refers to something that occurs infrequently or from time to time. A similar phrase that means the same thing is "now and again," which means something happens irregularly or sporadically. Lastly, we have "from time to time," which means something happens occasionally or irregularly.