source 1998 Cohen--Miyaji--Ono "Efficient elliptic curve exponentiation using mixed coordinates", formula (6), plus common-subexpression elimination
compute XX = X1^2
compute YY = Y1^2
compute ZZ = Z1^2
compute S = 4 X1 YY
compute M = 3 XX+a ZZ^2
compute T = M^2-2 S
compute X3 = T
compute Y3 = M (S-T)-8 YY^2
compute Z3 = 2 Y1 Z1