What formula does this graph follow? Hyperbola with a "notch"...

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Hello stackexchange people!

In some simulations of mine (concerning geometrical optics) i found many functions to perfectly follow a hyperbolic graph but some of them just mischievously decided to put in a little notch somewhere in the middle. I expect the functions not to be too crazy, no series expansions. Maybe some of you have seen something like this sometime?

Zoomed out graph. Blue is the questioned function, red is the main hyperbola it follows Zoomed out. Blue is the questioned  function, red is the main hyperbola it follows

Zoomed in on the little notch

Zoomed in on the little notch

I'll also attach the used data as a box.com link: https://app.box.com/s/37gko532p4eig7n81n5mwl86gp70r90l

Any suggestions would be highly appreciated. I'm quite stuck there...