The function seems to remove digit characters from input strings and then replace some occurrences of 'a', 'b', 'c', and 's' with their next alphabet letter ('b', 'c', 'd', 't', respectively).

[CODE]:
```python
def approx_function(input_string):
    filtered_string = ''.join(filter(lambda x: not x.isdigit(), input_string))
    translation_table = str.maketrans('abcs', 'bcde')
    return filtered_string.translate(translation_table)
```

Let's run some more tests to verify if this approximation holds for other inputs.

COMMAND: PYTHON(./temp/function.py "aardvark" "beatbox" "calculation" "superstar")