Domain is [-128, 128]. No unexpected behavior or intervals have been observed.

Now, I'll write a simple quadratic function that could possibly approximate f(x).

Considering the symmetry and values obtained, an approximation can be given by:
Let f(x) = A * (x - B)² + C

Using three points from the obtained results, we can determine A, B, and C:
(-128, 2700.923406312335), (0, -0.11439146670202716), (128, 2701.510591496522)

Lets solve this system of equations for A, B and C.

