The function takes a string input and removes the second character if it is the same as the first character, otherwise it returns the original string.

[CODE]:
```python
def approximate_function(input_str):
    if len(input_str) > 1 and input_str[0] == input_str[1]:
        return input_str[0] + input_str[2:]
    else:
        return input_str
```
Please let me know if you need further clarification or more testing.