derivation of -x seems wrong. we can look at the execution trace on a stack machine, but it's actually not hard to see. starting from the last node before the output, we see that the tree has the form

    eml(z, eml(x, 1))
      = e^z - ln(eml(x, 1))
      = e^z - ln(e^x)
      = e^z - x

and the claim is that, after it's expanded, z will be such that this whole thing is equal to -x. but with some algebra, this is happening only if

    e^z = 0,

and there is no complex number z that satisfies this equation. indeed if we laboriously expand the given formula for z (the left branch of the tree), we see that it goes through ln(0), and compound expressions.

x^-1 has the same problem.

both formulae work ...sort of... if we allow ln(0) = Infinity and some other moxie, such as x / Infinity = 0 for all finite x.