
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:
Let's start by running the function on some different input values to understand its behavior. 

COMMAND: PYTHON(./temp7/function.py -128 0 128)
user:
Response: Function input - output pairs: (-128, 1327436096.0000002) (0, 2.5600000000000005) (128, 1330079838.72) 

assistant:
Let's try some more input values to get a better understanding of the function's behavior.

COMMAND: PYTHON(./temp7/function.py -64 64 96 -16 16 48 80)
user:
Response: Function input - output pairs: (-64, 82882352.64) (64, 83213319.67999999) (96, 420985815.04) (-16, 321780.48) (16, 327107.84) (48, 26346929.92) (80, 203075938.56) 

assistant:
It seems the function displays some quadratic-like behavior. Let's try more input values to confirm it.

COMMAND: PYTHON(./temp7/function.py -6 -3 3 6 12 24 30)
user:
Response: Function input - output pairs: (-6, 6255.88) (-3, 372.2500000000001) (3, 437.4700000000001) (6, 6590.4400000000005) (12, 103818.40000000001) (24, 1651214.0800000003) (30, 4026803.5599999996) 

assistant:
Based on the output values, the function seems to behave exponentially. Let's discover the base by evaluating the function at evenly spaced power of 2 values.

COMMAND: PYTHON(./temp7/function.py 2 4 8 16)
user:
Response: Function input - output pairs: (2, 97.80000000000001) (4, 1333.2800000000002) (8, 20651.52) (16, 327107.84) 

assistant:
It appears that the function is exponential, with a base close to 4. I will now try to provide a description of the function.

[DESCRIPTION]: The function f(x) behaves exponentially, with a base close to 4.

[DOMAIN]: The domain of the function is all real numbers between -128 and 128. There is no interval with unexpected behavior.

[CODE]: 
```python
def approx_function(x):
    return 4 ** x
```