Efficient SNARK recursion requires switching between pairing friendly elliptic curves. In most optimal approaches these curves would construct a cycle, but there are no such known cycles. Instead, we use non-native arithmetic to brute force the pairing computation at the cycle cut-off. We describe an approach for combining direct field extension with polynomial-based non-native arithmetic. This reduces pairing computation to bivariate polynomial identity testing using Schwartz-Zippel lemma.