The function appears to transform each character in the input string independently, while leaving numbers and special characters unchanged. The transformation is most likely applying a similar rule across characters, such as shifting them by a fixed position in the ASCII table or unicode.

[CODE]:
```python
def approx_function(input_str):
    output_str = ""
    for char in input_str:
        if char.isalpha():
            new_char = chr(((ord(char) - ord('A') + 3) % 26) + ord('A')) if char.isupper() else chr(((ord(char) - ord('a') + 3) % 26) + ord('a'))
        else:
            new_char = char
        output_str += new_char
    return output_str
```

This code approximates the behavior of the function by shifting each alphanumeric character by a fixed position (3 in this case) in the alphabet, while leaving numbers and special characters unchanged.