u12=(SQRT(b1*x+a1)*SQRT(b2*x+a2)*SQRT(b3*y+a3)*SQRT(b4*y+a4)+SQRT(b1*y+a1)*SQ~
RT(b2*y+a2)*SQRT(b3*x+a3)*SQRT(b4*x+a4))/(x-y)

u13=(SQRT(b1*x+a1)*SQRT(b2*y+a2)*SQRT(b3*x+a3)*SQRT(b4*y+a4)+SQRT(b1*y+a1)*SQ~
RT(b2*x+a2)*SQRT(b3*y+a3)*SQRT(b4*x+a4))/(x-y)

u23=(SQRT(b1*x+a1)*SQRT(b2*y+a2)*SQRT(b3*y+a3)*SQRT(b4*x+a4)+SQRT(b1*y+a1)*SQ~
RT(b2*x+a2)*SQRT(b3*x+a3)*SQRT(b4*y+a4))/(x-y)

IHAT(0)=4*R_F((u12+u13)*(u12+u23),(u12+u13)*(u13+u23),(u12+u23)*(u13+u23))

IHAT(-e1)=2*b1*(2*b1*(a1*b3-a3*b1)*(a2*b3-a3*b2)*(a2*b4-a4*b2)*SQRT(b1*x+a1)*~
SQRT(b1*y+a1)*(SQRT(b1*x+a1)*SQRT(b4*y+a4)+SQRT(b1*y+a1)*SQRT(b4*x+a4))*R_D((~
u12+u13)*(u13+u23),(u12+u23)*(u13+u23),(u12+u13)*(u12+u23))-3*(2*b2*(a1*b3-a3~
*b1)*SQRT(b1*y+a1)*(SQRT(b1*x+a1)*SQRT(b1*y+a1)*SQRT(b4*x+a4)+b1*x*SQRT(b4*y+~
a4)+a1*SQRT(b4*y+a4))*R_F((u12+u13)*(u12+u23),(u12+u13)*(u13+u23),(u12+u23)*(~
u13+u23))+b1*(SQRT(b1*x+a1)*SQRT(b1*y+a1)*(SQRT(b2*x+a2)*SQRT(b3*y+a3)-SQRT(b~
2*y+a2)*SQRT(b3*x+a3))-(b1*y+a1)*SQRT(b2*x+a2)*SQRT(b3*x+a3)+b1*x*SQRT(b2*y+a~
2)*SQRT(b3*y+a3)+a1*SQRT(b2*y+a2)*SQRT(b3*y+a3))))/(3*(a1*b2-a2*b1)*(a3*b1-a1~
*b3)*SQRT(b1*x+a1)*SQRT(b1*y+a1)*(SQRT(b1*x+a1)*SQRT(b4*y+a4)+SQRT(b1*y+a1)*S~
QRT(b4*x+a4)))

u15=SQRT((a1*(a2*b1*b3*b4-a4*b1*b2*b3+b4*u12^2)-b1*(a2*a3*b1*b4-a4*(a3*b1*b2-~
u12^2)))/(a1*b4-a4*b1))

q15=u15*SQRT(b4*x+a4)*SQRT(b4*y+a4)/(SQRT(b1*x+a1)*SQRT(b1*y+a1))

s15=(SQRT(b1*x+a1)*SQRT(b2*y+a2)*SQRT(b3*y+a3)*(b4*x+a4)+SQRT(b1*y+a1)*SQRT(b~
2*x+a2)*SQRT(b3*x+a3)*(b4*y+a4))/((x-y)*SQRT(b1*x+a1)*SQRT(b1*y+a1))

b15=(u12+u15)*(u13+u15)*(u15+u23)*(a1*b5-a5*b1)/((a1*b2-a2*b1)*(a1*b3-a3*b1)*~
(a1*b4-a4*b1))

IHAT(-e5)=4*b5*(3*b5*(b15+q15+s15)*(a1*b5-a5*b1)^2*R_C(1,(b15+q15+s15)^2*(a1*~
b5-a5*b1)*(a2*b5-a5*b2)*(a3*b5-a5*b3)*(a5*b4-a4*b5)/(a1*b15*b5*(q15+s15)+a2*b~
5*(a3*b5-a5*b3)*(a4*b5-a5*b4)-a5*(a3*b2*b5*(a4*b5-a5*b4)-a4*a5*b2*b3*b5+a5^2*~
b2*b3*b4+b1*b15*(q15+s15)))^2+1)-(3*b1*(a1*b5-a5*b1)*R_F((u12+u13)*(u12+u23),~
(u12+u13)*(u13+u23),(u12+u23)*(u13+u23))+b5*(a1*b2-a2*b1)*(a1*b3-a3*b1)*(a4*b~
1-a1*b4)*R_J((u12+u13)*(u12+u23),(u12+u13)*(u13+u23),(u12+u23)*(u13+u23),u12*~
(u13+u23)+u13*u23+u15^2))*(a1*b15*b5*(q15+s15)+a2*b5*(a3*b5-a5*b3)*(a4*b5-a5*~
b4)-a5*(a3*b2*b5*(a4*b5-a5*b4)-a4*a5*b2*b3*b5+a5^2*b2*b3*b4+b1*b15*(q15+s15))~
))/(3*(a1*b15*b5*(q15+s15)+a2*b5*(a3*b5-a5*b3)*(a4*b5-a5*b4)-a5*(a3*b2*b5*(a4~
*b5-a5*b4)-a4*a5*b2*b3*b5+a5^2*b2*b3*b4+b1*b15*(q15+s15)))*(a1*b5-a5*b1)^2)

u10=SQRT(-(a1^2*b2*b3*b4-a1*b1*b2*(a3*b4+a4*b3)+b1*(a3*a4*b1*b2-u12^2))/b1)

q10=u10/(SQRT(b1*x+a1)*SQRT(b1*y+a1))

s10=(SQRT(b1*x+a1)*SQRT(b2*y+a2)*SQRT(b3*y+a3)*SQRT(b4*y+a4)+SQRT(b1*y+a1)*SQ~
RT(b2*x+a2)*SQRT(b3*x+a3)*SQRT(b4*x+a4))/((x-y)*SQRT(b1*x+a1)*SQRT(b1*y+a1))

b10=b1*(u10+u12)*(u10+u13)*(u10+u23)/((a1*b2-a2*b1)*(a1*b3-a3*b1)*(a4*b1-a1*b~
4))

IHAT(e1)=4*(3*b1^2*(b10+q10+s10)*R_C(1,1-b1*b2*b3*b4*(b10+q10+s10)^2/(b1*b10*~
(q10+s10)+b2*b3*b4)^2)+(a1*b2-a2*b1)*(a1*b3-a3*b1)*(a4*b1-a1*b4)*(b1*b10*(q10~
+s10)+b2*b3*b4)*R_J((u12+u13)*(u12+u23),(u12+u13)*(u13+u23),(u12+u23)*(u13+u2~
3),u10^2+u12*(u13+u23)+u13*u23))/(3*b1^2*(b1*b10*(q10+s10)+b2*b3*b4))