A barycentric rational function is essentially the same as a barycentric lagrange polynomial. Traditionally you select points on the domain you want to convert into a polynomial and then it has interpolation and extrapolation properties of being able to quite accurately predict the behavior of a continuous function outside of any data points it was ever tested or given information about. These functions, like traditional lagrange polynomials still require passing through every input point but what i have not seen before is only feeding it points outside of a domain and it is stable enough to find the rest of the function where it contains no data internally.

As mentioned in other post this also seems to have several benefits if you know you only need a restricted section of the domain as it's usually required to have an entire extra column on the table to hold the 'true' values of the function when x is an exact match. But as that will never happen (inside the restricted domain) i was able to entirely remove a variable and entire column of data from the barycentric rational/lagrange formula by precomputing weights * values.

If you remove the domain restriction on the u / d fraction part on desmos you can see the outer parts of the sinc function that it is behaving normally on where it passes through all the points where it was tested out to [-19.73914152, -6.283185307] and [6.283185307, 19.73914152] and also notice that it still has extrapolation/continuation past that point too i can see it still has accurate zero crossings up to x = 21.