The function appears to reverse the input string and replace every other character, starting from the first character, with the letter 'y'. For digits, the function reverses the input string but does not replace the characters.

[CODE]:
```python
def approximate_function(input_string):
    reversed_string = input_string[::-1]
    output_string = ""

    for i, char in enumerate(reversed_string):
        if i % 2 == 0:
            if char.isdigit():
                output_string += char
            else:
                output_string += "y"
        else:
            output_string += char

    return output_string
```

Let's run this approximation on a few more inputs to confirm the behavior.

COMMAND: PYTHON(./temp/function.py "happy" "algorithm" "!@#$%^&*()" "mixed123")