x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, 
x_3*x_7*(2*x_1*x_7^2+3*x_4)
x_4*x_7*(4*x_1*x_7^2+x_4)
x_3*x_8+x_5*x_7
x_4*x_8+x_6*x_7
2*x_1*x_3*x_7^3-3*x_2*x_3*x_7+x_3*x_7+x_5*x_8
16*x_1*x_4*x_7^3-6*x_2*x_4*x_7-3*x_3^2*x_7+2*x_6*x_8+24*x_7
