Feigenbaum Alpha and Delta

I've begun the long and tedious process of combining and simplifying the mathematical equations that I obtained from my Brute Force program. Unfortunately, computer power has yet to be able to interpret data or balance equations.

Here's one such equation I've stumbled upon thus far though, more or less calculating Feigenbaum's Delta Constant from his Alpha Constant:

Feigenbaum Delta ~= (((Feigenbaum Alpha)^3)^(2^(1/2 (1 + sqrt(5)))) + tanh(1/2 (1 + sqrt(5))))/(10^3)

{Delta = 4.66920160910299067185320382..., Alpha = 2.50290787509589282228390287321821578...}

...which is the same as:

𝛿 ~= ^{((α3)(2φ) + tanh(φ))}/_10³

{φ = ^{(1 + sqrt(5))}/₂}

The equation's result differs by 0.00000002661406623421073579, or 0.00000057%. This could be either due to the imprecision of computer mathematics, or the existence of some infinitesimal missing piece of the equation, or the fact that the constants themselves are based upon measurements of chaotic systems, and therefore have limited precision.