Based on the experiments, we have the following input-output pairs for the function:

(-128, 64440.54030166402)
(-100, 39200.01932593027)
(-50, 9650.319596894531)
(0, 0.6250247825708364)
(50, 50049.341139473254)
(100, 199600.77738517747)
(128, 326809.6297627049)

Now, let's proceed with the description of the function.

[DESCRIPTION]:
The function appears to be non-linear and exhibits different behaviors in different intervals. It starts with a large positive value for negative inputs, then transitions to smaller positive values near zero, and finally increases rapidly for positive inputs.

[DOMAIN]:
The domain of the function includes all numerical values. However, there is an interval around x = 0 where the function displays unexpected behavior. This is where the function's output approaches a significantly smaller value compared to the neighboring inputs.

[CODE]:
Based on the observations, we can approximate the behavior of the function using a combination of exponential and linear functions. Here's some Python code that demonstrates the approximation:

```python
import math

def f(x):
    if x < 0:
        return math.exp(x) * constant1
    elif x == 0:
        return constant2
    else:
        return x * constant3

# Constants to be determined experimentally
constant1 = 10.0
constant2 = 0.6
constant3 = 5000.0
```

Please note that the actual behavior of the function may be more complex than this simple approximation.