
user:
Hi, your job is to interpret a function f(x) that is implemented in the ./temp7/function.py script. f(x) takes numerical inputs.
All you can do is call f(x) on a value of x by running PYTHON(./temp7/function.py value). 
Try to describe the function implemented by f(x) by running experiments on it. 
You can call the function on multiple inputs at a time by running PYTHON(./temp7/function.py value1 value2 value3 ...). 
You can run the function multiple times on the same input. We encourage testing a large range of values before writing a description. You can test values between [-128 and 128]. 
The output could be noisy and your goal is to find a good simple description of f(x) that explains most of the function behavior. f(x) may combine multiple different operations.
There may be an interval inside the domain where the function behaves differently. If that is the case, describe that interval.
Your description of the function should have three parts. 
First, [DESCRIPTION]: Describe what the function is doing in language. 
[DOMAIN]: What is the domain of the function? Is there an interval where the function displays unexpected behavior? What are the numeric bounds of that interval? What is going on there?
[CODE]: Write python code that approximates the behavior of the function. 
assistant:
I will start by running experiments to understand the behavior of the function implemented in the ./temp7/function.py script.

COMMAND: PYTHON(./temp7/function.py -128 -64 0 64 128)
user:
Response: Function input - output pairs: (-128, 5.7921465825585345) (-64, 4.08246051551232) (0, 2.407853417441524) (64, 7.149142781625331) (128, 0.2977811424908925) 

assistant:
Let's test the function with more input values to understand the behavior of the function better.

COMMAND: PYTHON(./temp7/function.py -100 -50 -10 5 10 20 50 100)
user:
Response: Function input - output pairs: (-100, 5.792146582558505) (-50, 4.100000000000009) (-10, 7.149142781625318) (5, 0.5862214151805651) (10, 0.2977811424908876) (20, 4.100000000000002) (50, 1.050857218374679) (100, 0.29778114249088716) 

assistant:
Based on the results so far, it seems that the function behaves differently for negative, zero, and positive input values. Let's run more experiments to isolate this behavior.

COMMAND: PYTHON(./temp7/function.py -75 -25 -15 2 8 16 40)
user:
Response: Function input - output pairs: (-75, 4.137586544991411) (-25, 4.967831642429627) (-15, 8.0) (2, 7.902218857509112) (8, 7.149142781625317) (16, 0.29778114249088716) (40, 5.792146582558459) 

assistant:
Based on the experiments, I can now provide a description of the function.

[DESCRIPTION]: The function appears to be a nonlinear piecewise function that has different behaviors for negative, zero, and positive input values. The function varies non-linearly when the input is positive. When the input is 0, the output is near 2.4. For negative input values, the function seems to reach a maximum value of 8.0 at -15. The behavior of the function beyond the range tested has not been determined.

[DOMAIN]: The tested domain of the function is [-128, 128]. There are two intervals with distinct behavior:
- Negative interval: [-128, -1), where the function reaches a maximum of 8.0 at -15
- Positive interval: (0, 128], where the function varies non-linearly

[CODE]:
```python
def approx_function(x):
    if x < 0:
        return 8 - 0.1375865 * x if x > -15 else 8
    elif x == 0:
        return 2.4
    else:
        return 7.9 - 0.2977811 * x
```