The function alternates the letters 'e' and 'o' with 'i' and 'l', respectively.

[CODE]:
```python
def approximate_function(input_string):
    return input_string.replace('e', 'i').replace('o', 'l')
```

To further confirm, let's test some more inputs to see if the approximation holds true.

COMMAND: PYTHON(./temp/function.py "one" "two" "three" "four" "five")