The function replaces each letter in the input string with the letter that is two positions ahead of it in the alphabet, wrapping around when necessary (e.g., 'z' -> a'). Numeric characters remain unchanged.

[CODE]: 
```python
def approx_function(s):
    result = ""
    for c in s:
        if c.isalpha():
            shift = 2
            char = chr(((ord(c) - ord('A') + shift) % 26) + ord('A')) if c.isupper() else chr(((ord(c) - ord('a') + shift) % 26) + ord('a'))
            result += char
        else:
            result += c
    return result
```
Note that this is an approximation of the behavior of the function and there might be slight differences in edge cases.