source 2010 Costello--Lange--Naehrig
compute A = Z1^2
compute B = Z2^2
compute C = (Z1 + Z2)^2-A-B
compute D = X1 Z2
compute E = X2 Z1
compute F = Y1 B
compute G = Y2 A
compute H = D - E
compute I = 2 (F - G)
compute II = I^2
compute J = C H
compute K = 4 J H
compute X3 = 2 II - (D + E) K
compute JJ = J^2
compute Y3 = ((J + I)^2 - JJ - II) (D K - X3) - F K^2
compute Z3 = 2 JJ