Trying to end my loop after err is less than 1e-10.

I am trying to end my loop after the err is less than 1e-10.

Here is my code:

clear; 
clc;

syms x y;

%Declare Function
f(x,y)=x+2*y-2;
g(x,y)=x^2+4*y^2-4;

%Jacobian Matrixes
f_x(x,y)=diff(f,x);
f_y(x,y)=diff(f,y);

g_x(x,y)=diff(g,x);
g_y(x,y)=diff(g,y);

%Jacobian Matrix 
jac1=[f_x f_y; g_x g_y];

%Initial Guess and Max Iterations
x1=1;y1=2;
max=25;
tol=1e-10;

fprintf("=====================================================================================\n");
fprintf("The numbers displayed below are the intermediate points starting from x^1 until x^25.\n"); 
fprintf("The number displayed below the intermediate points is the error for that point.\n"); 
fprintf("=====================================================================================\n");

for i=1:max  
    jac = jac1(x1,y1);
    ijac = inv(jac);
    
    xx = double([x1;y1]-(ijac*[f(x1,y1);g(x1,y1)]));
    errorpoint=(-ijac)*([f(x1,y1);g(x1,y1)]);
    err=norm(xx-[x1,y1]);
    
    x1=double(xx(1));
    y1=double(xx(2));
    
    fprintf("\n");
    fprintf("Intermediate Point:%.10f\n", xx);
    fprintf("\n");
    
    fprintf("Error Point:%.10f\n", errorpoint)
    fprintf("\n");
    fprintf("=====================================================================================\n")
    
    result(i,1:2)=[x1,y1];
    
    if err<tol
        break
    end
end

Here is my output:

=====================================================================================

The numbers displayed below are the intermediate points starting from x^1 until x^25.

The number displayed below the intermediate points is the error for that point.

=====================================================================================

Intermediate Point:-0.8333333333

Intermediate Point:1.4166666667

Error Point:-1.8333333333

Error Point:-0.5833333333

=====================================================================================

Intermediate Point:-0.1893939394

Intermediate Point:1.0946969697

Error Point:0.6439393939

Error Point:-0.3219696970

=====================================================================================

Intermediate Point:-0.0150791353

Intermediate Point:1.0075395677

Error Point:0.1743148041

Error Point:-0.0871574020

=====================================================================================

Intermediate Point:-0.0001120013

Intermediate Point:1.0000560006

Error Point:0.0149671340

Error Point:-0.0074835670

=====================================================================================

Intermediate Point:-0.0000000063

Intermediate Point:1.0000000031

Error Point:0.0001119950

Error Point:-0.0000559975

====================================================================================

Intermediate Point:-0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000063

Error Point:-0.0000000031

=====================================================================================

Intermediate Point:-0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

===================================================================================

Intermediate Point:-0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:-0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:-0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:-0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

===================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

=====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

====================================================================================

Intermediate Point:0.0000000000

Intermediate Point:1.0000000000

Error Point:0.0000000000

Error Point:0.0000000000

====================================================================================

After manually doing the math the code should stop after the 6th iteration. But i cannot figure out how to stop my loop when the err is less than 1e-10.

Answer 1

[Image Analyst]

I guess it's never less than that. Print out more decimal places:

fprintf("Error Point:%.15f\n", errorpoint)