source 2009 Hisil--Wong--Carter--Dawson, formula (9), plus substitutions U = XX, V = ZZ, W = R/2, plus Z3 expansion using Z1=1
assume Z1 = 1
compute YY1 = Y1^2
compute X3 = Y1 R1
compute Z3 = 1 - XX1^2
compute XX3 = X3^2
compute ZZ3 = Z3^2
compute R3 = (X3+Z3)^2 - XX3 - ZZ3
compute Y3 = 2 YY1^2 - a XX3 - ZZ3