source 1998 Cohen--Miyaji--Ono "Efficient elliptic curve exponentiation using mixed coordinates", plus Z1=1, plus Z2=1, plus common-subexpression elimination
unified
assume Z1 = 1
assume Z2 = 1
compute u = Y2-Y1
compute uu = u^2
compute v = X2-X1
compute vv = v^2
compute vvv = v vv
compute R = vv X1
compute A = uu-vvv-2 R
compute X3 = v A
compute Y3 = u(R-A)-vvv Y1
compute Z3 = vvv
