source 2002 Billet--Joye "The Jacobi model of an elliptic curve and side-channel analysis", page 6, plus specialization to Z1=1 and Z2=1
assume Z1 = 1
assume Z2 = 1
compute T7 = Y1+X1
compute T8 = Y2+X2
compute T2 = Y1 Y2
compute T7 = T7 T8
compute T7 = T7-T2
compute T5 = X1 X2
compute T6 = T5
compute X3 = T7-T6
compute T1 = X1+X2
compute T3 = T1^2
compute T6 = 2 T6
compute T3 = T3-T6
compute T3 = T3 T6
compute T4 = a T6
compute T2 = T2+T4
compute T8 = T5^2
compute T5 = T8+1
compute T2 = T2 T5
compute Y3 = T2+T3
compute Z3 = 1-T8