Based on the new output values, it seems that the function starts behaving differently when the input value is above 80. The output values are increasing as the input values increase within this range. 

[DESCRIPTION]:
The function primarily produces outputs in the range of ~61.8 to ~62.1 for input values between -128 and 80. For input values above 80, the output values increase linearly with the input values.

[DOMAIN]:
The domain of the function appears to be valid for all provided inputs from -128 to 128. The function exhibits different behavior for input values greater than 80 within the domain.

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

```python
def approx_function(x):
    if x > 80:
        return 61.8 + 0.17 * (x - 80)
    else:
        return 61.8 + (61.9 - 61.8) / (1 +  ((x - 0) / 0.1) ** 2)
```

This code assumes that for x > 80, the output is a linear function of the input with a slope of approximately 0.17. The else part is an approximation of the function using a logistic function (sigmoid curve) for the input values between -128 and 80. Note that this approximation is not perfect and is merely an attempt to describe the observed behavior of the function.