source 2007 Bernstein--Lange; derived from 2006 Doche--Icart--Kohel "Efficient scalar multiplication by isogeny decompositions", page 197, middle display, by substitution Z2=1, simplification, projectification, clearing denominators, common-subexpression elimination
compute A = Y1 ZZ2-Y2 ZZ1
compute AA = A^2
compute X2Z1 = X2 Z1
compute B = X1 Z2-X2Z1
compute C = B Z2
compute E = C Z1
compute EE = E^2
compute F = E C
compute D = F X1
compute U = AA-a EE-D-X2Z1 E B
compute X3 = 2 U
compute Y3 = 2 ((E+A)^2-EE-AA) (D-U)-Y1 (2 F)^2
compute Z3 = 2 EE
compute ZZ3 = Z3^2