The function appears to return the count of specific uppercase letter combinations within the input string, where the count is represented as a lower case word. Currently, the combinations identified are "C" and "BC". If neither of these combinations are present in the input, 'none' is returned. 

[CODE]:
```python
def approx_function(input_str):
    count_C = input_str.count("C")
    count_BC = input_str.count("BC")

    if count_C:
        return str(count_C) + " occurrence(s) of C"
    elif count_BC:
        return str(count_BC) + " occurrence(s) of BC"
    else:
        return "none"
```

Note: The provided approximation function returns the count as "occurrence(s)" instead of words like "zero", "one", "two", etc., as seen in the original function outputs.