How to check if two equations are equal

Hello, I'm trying to verify if an equation is time-invariant or not time-invariant. So I'm putting two equations in a for loop to see if the values of each equation are equal. In theory, these values should be equal, but it is outputting, not time-invariant. Any help?

clear
syms t

x1(t)=cos(t);
y1(t)=1-2*x1(t-1);

x2(t)=cos(t-3);
y2(t)=1-2*x2(t-1);

for t=-pi():.1:pi()
    Check_Y=y1(t-3);
    Check_X=y2(t);
    if Check_X~=Check_Y
       disp('Not time invarient')
       break
    end
    if t==-pi()+6.2
       disp('Time invarient')
    end
end

t=-pi():.1:pi();

figure
subplot(3,1,1)
plot(t,y1(t))
title('x(t):y(t)')

subplot(3,1,2)
plot(t,y2(t))
title('x(t-3):y(t)')

subplot(3,1,3)
plot(t,y1(t-3))
title('y(t-3)')

Answer 1

[VBBV]

clear
syms t
x1(t)=cos(t);
y1(t)=1-2*x1(t-1);
x2(t)=cos(t-3);
y2(t)=1-2*x2(t-1);
for t=-pi():.1:pi()
  Check_Y=vpa(y1(t-3),2);
  Check_X=vpa(y2(t),2);
  if Check_X~=Check_Y
     disp('Not time invarient')
     break
  end
  if t==-pi()+6.2
     disp('Time invarient')
  end
end
t=-pi():.1:pi();
figure
subplot(3,1,1)
plot(t,y1(t))
title('x(t):y(t)')
subplot(3,1,2)
plot(t,y2(t))
title('x(t-3):y(t)')
subplot(3,1,3)
plot(t,y1(t-3))
title('y(t-3)')

Try with vpa for check variables.