source 2015 Renes--Costello--Batina "Complete addition formulas for prime order elliptic curves", Appendix A.1 parameter b3 assume b3 = 3 b compute t0 = X1 * X2 compute t1 = Y1 * Y2 compute t2 = Z1 * Z2 compute t3 = X1 + Y1 compute t4 = X2 + Y2 compute t3 = t3 * t4 compute t4 = t0 + t1 compute t3 = t3 - t4 compute t4 = X1 + Z1 compute t5 = X2 + Z2 compute t4 = t4 * t5 compute t5 = t0 + t2 compute t4 = t4 - t5 compute t5 = Y1 + Z1 compute X3 = Y2 + Z2 compute t5 = t5 * X3 compute X3 = t1 + t2 compute t5 = t5 - X3 compute Z3 = a * t4 compute X3 = b3 * t2 compute Z3 = X3 + Z3 compute X3 = t1 - Z3 compute Z3 = t1 + Z3 compute Y3 = X3 * Z3 compute t1 = t0 + t0 compute t1 = t1 + t0 compute t2 = a * t2 compute t4 = b3 * t4 compute t1 = t1 + t2 compute t2 = t0 - t2 compute t2 = a * t2 compute t4 = t4 + t2 compute t0 = t1 * t4 compute Y3 = Y3 + t0 compute t0 = t5 * t4 compute X3 = t3 * X3 compute X3 = X3 - t0 compute t0 = t3 * t1 compute Z3 = t5 * Z3 compute Z3 = Z3 + t0