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  • $\begingroup$ However, the Log-Exp pair can be replaced with any other functional pair such that $f(g(x))=x$ and $f(x)>0$ for domain of interest. For instance g[x]=Sqrt[x] and f[x]=x^2. $\endgroup$
    – yarchik
    Commented Oct 30, 2019 at 10:41
  • $\begingroup$ @yarchik Of course, but with the same drawback more or less amplified (based on the slope of $g$). Bottom line: what is the missing information that is sought between the known points? If the purpose of interpolating is to take the derivative, that could be a very bad strategy. $\endgroup$
    – anderstood
    Commented Oct 30, 2019 at 12:10
  • 1
    $\begingroup$ The problem is intrinsically unsymmetrical: zero is a line that must not be crossed, but there is no upper limit. Looking at the function, the peaks are rounded, but the valleys are nearly flat. The Log method reflects this, while you seem to insist that a proper method should not. $\endgroup$
    – John Doty
    Commented Oct 30, 2019 at 19:25