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The calculation is done by triangulating three pieces of data: centre of the satellite (moon), McDonald observatory in Texas, user position of the app.

The McDonald observatory provides an updated distance to the moon in real time.
The number is the result of the above calculation using the coordinates of the observatory in Texas as the coordinates.
The ioxyz0 app draws on the calculation of this distance by replacing the coordinates of the observatory with the real-time coordinates of the user by following the user’s movements.
The user then becomes a mobile extension of the observatory in this scheme.
*the observatory’s calculation database is opensource.

The McDonald observatory itself makes use of the algorithm developed by Vladimir Agafonkin and Robin Schneider. https://aa.quae.nl/en/reken/hemelpositie.html
This algorithm is based on the calculations of Dr. Louis Strous.
[…] I calculated the position of the Moon (λ, β, ) for every day between 1950 and 2050 according to the above method and also according to a much more accurate method (of which the above method includes only the very largest terms). The largest error in λ was 2.57 degrees (standard deviation 1.04 degrees), that in β 0.81 degrees (standard deviation 0.31 degrees), and that in 7645 km (standard deviation 3388 km).