# Polynomial evaluation at all different points

I have a polynomial $$f(x_1,\ldots,x_{50})$$ of 50 variables over binary field $$GF(2)$$. I want to evaluate at all $$2^{50}$$ points and check how many of them are 0. Ofcourse we can evaluate at all points and check them. Can we do faster than this using some memory?

If you're happy with finding the fraction of evaluation points over which the polynomial vanishes, up to an additive constant $$\epsilon$$, then you can trivially evaluate at enough random points and take the empirical estimate.