Question: Data Fit problem

There are two data txt files:x0-y0.txt and x1-y1.txt,every one has two columns.
So, two functions can be made from the data,named y0=y0(x0) and y1=y1(x1).
I just want (y0-y1)/y0 at the same x coordinate.
Because it's too difficult to get it directly,I choose the curve fit method.
First,I used the command CurveFitting[ThieleInterpolation] to get two functions.
And then pointplot the (y0-y1)/y0 at the same x0 coordinate.
Surprisingly,the plot is discontinued.
Between the x coordinate 0.45 and 0.6,it seems that there is a discontinuous point.
I think the problem is that the difference between y0 and y1 is very small,so the Digits was redefined for 30.
But the problem is still exist.
Help,thank you in advance.

x0-y0.txt  x1-y1.txt

 

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