Yeah, you're right on all of that. I think there have been recent breakthroughs on quadratic (I think at ARITH 23? Yep, just looked, it's the best paper: https:

Yeah, you're right on all of that. I think there have been recent breakthroughs on quadratic (I think at ARITH 23? Yep, just looked, it's the best paper: https://arith2023.arithsymposium.org/program.html https://arith2023.arithsymposium.org/program.html) so hopefully this will become more accessible with time. Though OTOH RLibM-style techniques can get you very short polynomials, to the point that it's hard to imagine beating them by much given the high cost of division operations (like 3x a multiplication).