How can I simplify the division of big numbers?

My code is as:

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clear all

close all

clc

syms T_1 T_2 T_3 T_4 N_1 N_2 N_3 N_4 

%%Initioal Conditions

eps=1;L=2.5;l_13=1.5;g=9.8;ra_1=0.5;ra_2=0.8;ra_3=0.6;ra_4=0.7;m_1=10;m_2=20;m_3=15;m_4=17;alpha_12=-pi/3;

alpha_34=-pi/3;Phi=-pi/3;Theta_1=-pi/2;Theta_2=0;Theta_3=0;Theta_4=-pi/2;

%%Equations

Deltaalpha=alpha_34-alpha_12;

alpha_13=-asin(L*sin(Deltaalpha)/(2*l_13));

SigmaF_x =T_1*cos(Theta_1) + T_2*cos(Theta_2) + T_3*cos(Theta_3) + T_4*cos(Theta_4) + N_1*cos(Phi)*sin(Theta_1) + N_2*cos(Phi)*sin(Theta_2) + N_3*cos(Phi)*sin(Theta_3) + N_4*cos(Phi)*sin(Theta_4);

SigmaF_z =N_1*cos(Phi)*cos(Theta_1) - g*m_2 - g*m_3 - g*m_4 - T_1*sin(Theta_1) - T_2*sin(Theta_2) - T_3*sin(Theta_3) - T_4*sin(Theta_4) - g*m_1 + N_2*cos(Phi)*cos(Theta_2) + N_3*cos(Phi)*cos(Theta_3) + N_4*cos(Phi)*cos(Theta_4);

SigmaM_x =N_4*sin(Phi)*(l_13*sin(Phi + alpha_13) + L*sin(alpha_34)) - l_13*(g*m_4 + T_4*sin(Theta_4) - N_4*cos(Phi)*cos(Theta_4)) - l_13*(g*m_3 + T_3*sin(Theta_3) - N_3*cos(Phi)*cos(Theta_3)) + N_3*l_13*sin(Phi + alpha_13)*sin(Phi) + L*N_2*sin(Phi)*sin(alpha_12) + T_1*ra_1*sin(Phi)*sin(Theta_1) + T_2*ra_2*sin(Phi)*sin(Theta_2) + T_3*ra_3*sin(Phi)*sin(Theta_3) + T_4*ra_4*sin(Phi)*sin(Theta_4);

SigmaM_y =(l_13*sin(Phi + alpha_13) + L*sin(alpha_34))*(T_4*cos(Theta_4) + N_4*cos(Phi)*sin(Theta_4)) + L*(g*m_2 + T_2*sin(Theta_2) - N_2*cos(Phi)*cos(Theta_2)) + L*(g*m_4 + T_4*sin(Theta_4) - N_4*cos(Phi)*cos(Theta_4)) + l_13*sin(Phi + alpha_13)*(T_3*cos(Theta_3) + N_3*cos(Phi)*sin(Theta_3)) + L*sin(alpha_12)*(T_2*cos(Theta_2) + N_2*cos(Phi)*sin(Theta_2)) + T_1*ra_1*cos(Phi) + T_2*ra_2*cos(Phi) + T_3*ra_3*cos(Phi) + T_4*ra_4*cos(Phi);

SigmaM_z =T_1*ra_1*cos(Theta_1)*sin(Phi) - l_13*(T_4*cos(Theta_4) + N_4*cos(Phi)*sin(Theta_4)) - L*N_2*sin(Phi) - L*N_4*sin(Phi) - l_13*(T_3*cos(Theta_3) + N_3*cos(Phi)*sin(Theta_3)) + T_2*ra_2*cos(Theta_2)*sin(Phi) + T_3*ra_3*cos(Theta_3)*sin(Phi) + T_4*ra_4*cos(Theta_4)*sin(Phi);

sixthEq =N_2*T_1 - N_1*T_2;

seventhEq =N_3*T_2 - N_2*T_3;

%%Solve 

SOL=solve([SigmaF_x,SigmaF_z,SigmaM_x,SigmaM_y,SigmaM_z,sixthEq,seventhEq],[T_1,T_2,T_3,T_4,N_1,N_2,N_3]);

Result=vpa(SOL.T_1,3)

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Why the Result has a lot of big numbers; however, it easily can be seen that if Matlab divide these big numbers, the answers are not too big?!. For instance, the answer has numbers as big as 1e1493 divided by 1490?! but MatLab is unable to divide these numbers.

Regards

Answer 1

[Walter Roberson]

vpa(simplify(Result),3)

[Walter Roberson]

The expression has very nasty numeric properties, and you should expect more or less garbage answers up into 20000+ digits precision.

[Meysam E]

If Matlab simplify those divisions such as 1e2014/1e2010 the problem is solved!

[Walter Roberson]

No, I ran the calculation to 50000 digits of precision and it was still getting the wrong answer, with the order of magnitude changing significantly (sometimes worse) as the number of digits of precision increased. The equation is very bad numerically and any answer you are getting is almost certainly wrong.