Taylor series of upx function

[bo198214]

Can this solution be verified to be different from the approximation that Andrew came up with using linear equations for slog? The values for Dmitri's this solution appear very close to Andrew's approximation.

To me, it would seem as if the first couple of derivatives at x=-1,0 were the same for both solutions, than it is likely that they're the same solution, though the two could still diverge in the higher derivatives.

Thats always the difficulty with those numerical comparison. If the difference is small does that mean that they are equal?
Here is a really good counterexample. There are two methods two compute an iterational square root of \( \sqrt{2}^x \): regular iteration at the lower fixed point and regular iteration at the upper fixed point. The difference is in the order of \( 10^{-24} \). So you wouldnt have noticed it by usual numeric approximation.