Granted, but the claim in the abstract says:
>> computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations
And I don't see how this is true as to hypergeometric functions in a way that isn't shared by the approach in the paper.
> Finding a binary operation that can do this, like in TFA, is far more difficult, which is why it has not been done before.
> A function with 4 parameters can actually express not only any elementary function, but an infinity of functions with 3 parameters, e.g. by using the 4th parameter to encode an identifier for the function that must be computed.
These statements seem to be in direct conflict with each other; you can use the second parameter of a binary function to identify a unary function just as you can use the fourth parameter of a quaternary function to identify a trinary one.