The function appears to take an input string and output a word representing a number. The number appears to be the sum of modulo 3 of the index of the characters in the input string according to the English alphabet where "a" starts with 0. If the sum is 0, the output is "zero".

[CODE]:

```python
def approx_function(s):
    alpha = 'abcdefghijklmnopqrstuvwxyz'
    total = sum([(alpha.index(c) % 3) for c in s.lower()])
    
    number_words = {
        0: "zero",
        1: "one",
        2: "two",
        3: "three",
        4: "four",
        5: "five",
        6: "six",
        7: "seven",
        8: "eight",
        9: "nine",
        10: "ten",
        11: "eleven",
        12: "twelve",
        13: "thirteen",
        14: "fourteen",
        15: "fifteen",
        16: "sixteen",
        17: "seventeen",
        18: "eighteen",
        19: "nineteen",
        20: "twenty",
        21: "twenty-one",
        22: "twenty-two",
        23: "twenty-three",
    }
    
    return number_words[total]
```

Please note that this code is an approximation of the function's behavior based on the observations and may not be an exact replication of the original function.