The function replaces every occurrence of the letter 'a' (case-insensitive) with the letter 's' in the input string.

[CODE]:
```python
def approx_function(input_string):
    return input_string.replace('a', 's').replace('A', 'S')
```

To further confirm this, let's test a few more input strings that focus on the letter 'a'.

COMMAND: PYTHON(./temp/function.py "aaaa" "AaAa" "AbAcAdAe" "Aardvark")