source 2009 Bernstein--Kohel--Lange
parameter recipd
assume d recipd = 1
compute U = a X1 X1^2
compute V = Y1 Y1^2
compute W = Z1 Z1^2
compute A = (U-V)^2
compute B = (U-W)^2
compute C = (V-W)^2
compute D = A+C
compute E = A+B
compute X3 = recipd(U+V+W)(B+D)
compute Y3 = 2 U C-V(C-E)
compute Z3 = 2 V B-U(B-D)