Actually, I missed something basic. Maybe it stood out to you, PaulHoule, as it made the 3rd and 4th approximations worse than is possible, but in any case...

Actually, I missed something basic. Maybe it stood out to you, PaulHoule, as it made the 3rd and 4th approximations worse than is possible, but in any case... The 2nd approximation was minimax, but then I made a non-minimax approximation out of a minimax one, to get rid of error at the end of the input value range. It would have been possible to do that in a minimax way instead, by changing (increasing) the input value range for the approximation. Doing it just enough would move the last place where the error drops down to zero outwards to the end of the old input value range. I didn't think of that earlier.