Hi smichr,

I have updated my original gist:

https://gist.github.com/1582089

Here is a summary:

"""
import sympy as sp
import numpy as np

d, n = sp.symbols('d n', real=True, positive=True)
eps = sp.symbols('eps', real=True, positive=True)

jl_bound = 4 * sp.log(n) / (eps ** 2 / 2 - eps ** 3 / 3)

# solve the inverted expression as sympy is much faster as finding the 
roots of
# a polynomial and the point eps=0 is not interesting to us anyway.
solutions = sp.solve(sp.Equality(1 / d, 1 / jl_bound), eps)

sol = solutions[1]

sp.expand(sol, complex=True)

"""

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