Users might be confused by the notion of single vs. double precision used throughout this site and in Fractorium. They refer to two different data types used inside the program for performing calculations. The reason for supporting both dates back to the original flam3 code. Its authors experimented with different types to see what kind of outputs they would give vs. their relative performance. Fractorium did something similar and the result is what you see now with options to use single or double precision in both Fractorium and the command line programs.
Single is faster, but less precise. Double is slower but more precise. The latter will give the more correct output.
In practice, the difference in speed between the two on the CPU is negligible, so you should always use double for the CPU. However, GPUs are widely known to have major performance differences between single and double precision calculations. You should experiment with both data types on your GPU to get a feel for how each perform. If you have a faster GPU, then definitely use double precision. However, if you have a slower one, then stick with single.
One possible compromise is to use single in the interactive editor, then switch to double to see if there is any difference. If there is none, you can remain in single and also use it for the final render. If there is a difference, then you know you need to use double in both the interactive renderer and the final render dialog.
In the end, the trade off of quality vs. performance is up to you.