On Monday, 24 February 2014 11:34:22 UTC, Hans W Borchers wrote: > > This innocent looking test function appears to be so flat that only an > arbitrary precision solver will locate this root more exactly. >
I think what is required in this case is a more accurate implementation of the function itself! If you actually have a use case for such functions, please let me know as I've been (slowly) making some changes to the Distributions.jl, and one of the functions required is "log1pmx", a stable form of log(1+x) - x. I've got some draft code such that I've managed to get the error down to 2.5 ulps. It would be fairly straightforward to modify this to get an expression for g(x) = log(x+1) - x + x^2/2, and then your function could be written as g(x/sqrt(e) -1)
