source 1986 Chudnovsky--Chudnovsky "Sequences of numbers generated by addition in formal groups and new primality and factorization tests", page 415, formula (4.4i)
compute U1 = X1 Z2
compute U2 = X2 Z1
compute S1 = Y1 Z2
compute S2 = Y2 Z1
compute W = Z1 Z2
compute P = U2-U1
compute R = S2-S1
compute X3 = P(-(U1+U2)P^2+W R^2)
compute Y3 = (R(-2 W R^2+3(U1+U2)P^2)-P^3(S1+S2))/2
compute Z3 = W P^3