We describe deterministic algorithms which for a given depth-2 circuit F approximate the probability that on a random input F outputs a specific value &alpha;. Our approach gives an algorithm which for a given GF multivariate polynomial p and given &epsilon; > 0 approximates the number of zeros of p within a multiplicative factor 1+&epsilon;. The algorithm runs in time exp(exp(O( p log(n=ffl)))), where n is the size of the circuit. We also obtain an algorithm which given a DNF formula F and &epsilon; > 0 approximates the number of satisfying assignments of F within a factor of 1 + &epsilon; and runs in time exp(O((log(n/&epsilon;))^4))
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