The function takes a string input and applies a Caesar cipher-like transformation to the letters, shifting each letter by a distance-based value in the alphabet (e.g., 'a' goes to 'c', 'b' goes to 'd', etc.). Digits in the input string are reversed in order, and special characters and spaces remain unchanged.

[CODE]:
```python
def approx_function(s):
    result = []

    for c in s:
        if c.isalpha():
            shifted_c = chr(((ord(c) - ord('a') + 2) % 26) + ord('a'))
            result.append(shifted_c)
        elif c.isdigit():
            result.insert(0, c)
        else:
            result.append(c)

    return ''.join(result)
```

Let's test the function with more inputs before wrapping up.

COMMAND: PYTHON(./temp/function.py "Coding" "Cipher" "Task" "1234" "!@#")