After running the experiments, here are the input-output pairs:

(-128, -4406.85)
(-64, -2218.05)
(-32, -1123.65)
(-16, -576.45)
(-8, -302.85)
(-4, -166.05)
(-2, -97.65)
(-1, -63.45)
(0, -29.25)
(1, 26.18)
(2, 374.97)
(4, 1952.63)
(8, 8628.27)
(16, 36060.83)
(32, 147251.07)
(64, 594932.03)
(128, 2391495.87)

[DESCRIPTION]:
Based on the results, the function seems to be non-linear and produce outputs that increase rapidly as the input moves towards positive values. The function also appears to have different behavior for negative and positive inputs.

[DOMAIN]:
The domain of the function is [-128, 128]. There doesn't seem to be any unexpected behavior or unusual intervals within this range.

[CODE]:
Here is a python code that approximates the behavior of the function:

```python
def f(x):
    if x >= 0:
        return x**3 + 1
    else:
        return x**2 - x - 1
```
This code captures the different behavior for negative and positive inputs. For positive inputs, it raises the input to the power of 3 and adds 1. For negative inputs, it calculates the square of the input, subtracts the input itself, and subtracts 1.