source 2002 Brier--Joye "Weierstrass elliptic curves and side-channel attacks", formula (10) accompanied by note "7 multiplications plus 2 multiplications by a constant", plus common-subexpression elimination emphasizing squaring
parameter b2
assume b2 = 2 b
parameter b4
assume b4 = 4 b
compute XX = X1^2
compute ZZ = Z1^2
compute A = 2((X1 + Z1)^2 - XX - ZZ)
compute aZZ = a ZZ
compute X3 = (XX - aZZ)^2 - b2 A ZZ
compute Z3 = A (XX + aZZ) + b4 ZZ^2