# Floors and Ceilings and Cosines, Oh My!

**Geometry**Level 5

\[\begin{eqnarray} f\left( x \right) &=&\cos { \left( \pi \left\lfloor x \right\rfloor \right) } \left( { 2 }^{ x-\left\lfloor x \right\rfloor }-1 \right) \\\ g\left( x \right) &=&\cos { \left( \frac { \pi }{ 2 } \left\lfloor x \right\rfloor \right) } \left( { 2 }^{ \left\lceil x \right\rceil -x }-1 \right) \end{eqnarray}\]

The set of all real \(x\) such that \(0 \leq x \leq 2015\) and \(f(x) > g(x)\) is a union of disjoint intervals. What is the sum of the lengths of those intervals?

**Notations**:

-\(\left\lfloor x \right\rfloor \) denotes the greatest integer not exceeding \(x\). For example, \(\left\lfloor 2.123 \right\rfloor = 2\) and \(\left\lfloor 7 \right\rfloor = 7\)

-\(\left\lceil x \right\rceil \) denotes the smallest integer greater than or equal to \(x\). For example, \(\left\lceil 2.123 \right\rceil =3\) and \(\left\lceil 7 \right\rceil =7\)

###### Inspired by my favorite AMC-12 problem.

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