mathematics - Make 2008 from Φ (Golden Ratio)

I know that questions of the form "Use [arbitrary set of numbers] to make 2018" seem to be not very well recieved in the last days. That's why this puzzle is about making 2008.

But instead of using some randomly chosen numbers, you will use the most beautiful number I can imagine: $\Phi = \tfrac{1}{2} \left( 1 + \sqrt{5} \right)$ – the Golden Ratio.

To make 2008 you may use

• the operators $+$, $-$, $\cdot$, $/$



• exponentiation


• brackets $($ $)$

and any number of instances of $\Phi$. The answer with the least number of $\Phi$s will be accepted.

You may not use operators or functions other than in this list, so don't even ask for rounding ($\lfloor$ $\rfloor$, $\lceil$ $\rceil$) or logarithm ($\log_a (x)$). If you want to use roots, this is ok as long as you express them as exponent: $\sqrt[n]{x} = x^{\frac{1}{n}}$.

Answer

Score:

21

The solution:

$ \frac{x+x}{x} \cdot ( \frac{x+x+x+x}{x} + (\frac{x}{x} + (\frac{x+x+x}{x})^{ \frac{x+x}{x} })^ {\frac{x+x+x}{x}})$ where $x = \phi $.

Based on

$ 2 \cdot (4 + (1 + 3^2)^3) $