The function reverses the input string and then shifts the characters in the output string forwards or backwards based on whether they are alphabetic, numeric, or special characters.

[CODE]:
```
def approx_function(input_str):
    reversed_str = input_str[::-1]
    output_str = ""

    for char in reversed_str:
        if char.isalpha():
            output_str += chr(((ord(char) - 96 + 1) % 26) + 96)
        elif char.isnumeric():
            output_str += chr(((ord(char) - 48 + 1) % 10) + 48)
        else:
            output_str += chr(((ord(char) - 33 - 1) % 94) + 33)

    return output_str
```

Keep in mind that this is an approximation based on the tested inputs and may deviate slightly from the actual function in case of some inputs.