The function takes a string input and performs some operations on it. It seems to double the input string, remove any non-alphabetic characters, and then convert all the alphabetic characters to lowercase.

[CODE]:
```python
def f(x):
    x = x * 2
    x = ''.join([char.lower() for char in x if char.isalpha()])
    return x
```

This code approximates the behavior of the function based on the experimental results. However, keep in mind that this is just an approximation, and there may be additional operations or details in the actual implementation of the function.