https://mandeljs.hgreer.com/?;re=-0.751165720536567020384363...
(I don't know if this is a known compromise of your technique (I couldn't find it mentioned), but I occassionally get a ring of varying thickness centred in the render with an inverted coluring to the rest of the pixels, or sometimes a solid colour. It varies is size and comes and goes without an obvious correlation to zoom level.)
I'm representing complex numbers as (real_mantissa + i * imag_mantissa) * 2^exp where real_mantissa and imag_mantissa are themselves 32 bit floats, and I can reduce the frequency of the colored rings in my shader by keeping the mantissas around ~1000 instead of ~1 (and reducing the exponent to keep the value the same) so that they are less likely to go subnormal, but I can't seem to get rid of the colored rings entirely.
I don't actually know the pathway through the code from subnormal underflow -> colored rings, but if you run a CUDA renderer with the same algorithm, the rings appear when you set the flag for "round subnormal floats to zero."
fragColor = vec4(vec3(cos(c), cos(1.1214 * c) , cos(.8 * c)) / 2. + .5, 1.);