There are two main data sources in Cerridwen with slightly different precision characteristics.
Most data, like planetary position and rise/set times, is pulled directly from the Swiss Ephemeris library, whose authors claim a precision of 0.001 arc seconds, or less than 2.8x10-7 degrees.
Other data like new and full moon events are generated by Cerridwen’s algorithms. The results of these algorithms are guaranteed to be exact within 10-6 degrees, or 0.0036 arc seconds. This is in fact ensured by an assertion in the code.
Thus Cerridwen’s calculations are precise enough to get event times of the ascendant and of rise and set times down to the correct second.
Please note that the current implementation of the API server uses memoization for the moon data, generating a new response every 10 seconds only due to efficiency considerations. You can easily turn this off or modify this if you run your own API server, or just wait for the next version of Cerridwen that will be able to calculate new and full moons in a more efficient manner.