The function reverses the input string, changes the case of alphabetic characters (uppercase to lowercase, lowercase to uppercase), and directly reverses digits.

[CODE]: 
```python
def approx_function(input_str):
    reversed_str = input_str[::-1]
    transformed_str = ''
    for char in reversed_str:
        if char.isalpha():
            transformed_str += char.swapcase()
        elif char.isdigit():
            transformed_str += char
        else:
            transformed_str += char
    return transformed_str
```

Keep in mind, this is an approximation, and there might be some edge cases that are not covered by this code.