f=(y1+y2)(y1-y2)+(y1+y2)y3+(y1+y2)y4+(y1-y2)y4
= y1^2 - y2^2 + y1y3 + 2y1y4 + y2y3
= (y1+(1/2)y3+y4)^2 - y2^2 -(1/4)y3^2 + y2y3 -y3y4 - y4^2
= (y1+(1/2)y3+y4)^2 - (y2-(1/2)y3)^2 -y3y4 - y4^2
= (y1+(1/2)y3+y4)^2 - (y2-(1/2)y3)^2 -(y4+(1/2)y3)^2 + (1/4)y3^2
= z1^2 - z2^2 - z3^2 + (1/4)z4^2