source 2010 Costello--Lange--Naehrig
assume Z2 = 1
compute A = Z1^2
compute E = X2 Z1
compute G = Y2 A
compute H = (X1 - E)
compute I = (Y1 - G)
compute II = I^2
compute J = Z1 H
compute K = 2 J H
compute X3 = 2 II - (X1 + E) K
compute JJ = J^2
compute Y3 = ((J+ I)^2 - JJ - II) (X1 K - X3) - Y1 K^2
compute Z3 = 2 JJ