math_utils.py

from typing import Optional
from autogen import oai, DEFAULT_MODEL

_MATH_PROMPT = "{problem} Solve the problem carefully. Simplify your answer as much as possible. Put the final answer in \\boxed{{}}."
_MATH_CONFIG = {
    "model": DEFAULT_MODEL,
    "prompt": _MATH_PROMPT,
}


def solve_problem(problem: str, **config) -> str:
    """(openai<1) Solve the math problem.

    Args:
        problem (str): The problem statement.
        config (Optional, dict): The configuration for the API call.

    Returns:
        str: The solution to the problem.
    """
    params = {**_MATH_CONFIG, **config}
    response = oai.Completion.create({"problem": problem}, **params)
    results = eval_math_responses(oai.Completion.extract_text(response))
    return results.get("voted_answer"), response["cost"]


def remove_boxed(string: str) -> Optional[str]:
    """Source: https://github.com/hendrycks/math
    Extract the text within a \\boxed{...} environment.
    Example:

    > remove_boxed("\\boxed{\\frac{2}{3}}")

    \\frac{2}{3}
    """
    left = "\\boxed{"
    try:
        if not all((string[: len(left)] == left, string[-1] == "}")):
            raise AssertionError

        return string[len(left) : -1]
    except Exception:
        return None


def last_boxed_only_string(string: str) -> Optional[str]:
    """Source: https://github.com/hendrycks/math
    Extract the last \\boxed{...} or \\fbox{...} element from a string.
    """
    idx = string.rfind("\\boxed")
    if idx < 0:
        idx = string.rfind("\\fbox")
        if idx < 0:
            return None

    i = idx
    right_brace_idx = None
    num_left_braces_open = 0
    while i < len(string):
        if string[i] == "{":
            num_left_braces_open += 1
        if string[i] == "}":
            num_left_braces_open -= 1
            if num_left_braces_open == 0:
                right_brace_idx = i
                break
        i += 1

    if right_brace_idx is None:
        retval = None
    else:
        retval = string[idx : right_brace_idx + 1]

    return retval


def _fix_fracs(string: str) -> str:
    """Source: https://github.com/hendrycks/math
    Reformat fractions.
    Examples:
    >>> _fix_fracs("\\frac1b")
    \frac{1}{b}
    >>> _fix_fracs("\\frac12")
    \frac{1}{2}
    >>> _fix_fracs("\\frac1{72}")
    \frac{1}{72}
    """
    substrs = string.split("\\frac")
    new_str = substrs[0]
    if len(substrs) > 1:
        substrs = substrs[1:]
        for substr in substrs:
            new_str += "\\frac"
            if substr[0] == "{":
                new_str += substr
            else:
                try:
                    if not len(substr) >= 2:
                        raise AssertionError
                except Exception:
                    return string
                a = substr[0]
                b = substr[1]
                if b != "{":
                    if len(substr) > 2:
                        post_substr = substr[2:]
                        new_str += "{" + a + "}{" + b + "}" + post_substr
                    else:
                        new_str += "{" + a + "}{" + b + "}"
                else:
                    if len(substr) > 2:
                        post_substr = substr[2:]
                        new_str += "{" + a + "}" + b + post_substr
                    else:
                        new_str += "{" + a + "}" + b
    string = new_str
    return string


def _fix_a_slash_b(string: str) -> str:
    """Source: https://github.com/hendrycks/math
    Reformat fractions formatted as a/b to \\frac{a}{b}.
    Example:
    >>> _fix_a_slash_b("2/3")
    \frac{2}{3}
    """
    if len(string.split("/")) != 2:
        return string
    a_str = string.split("/")[0]
    b_str = string.split("/")[1]
    try:
        a = int(a_str)
        b = int(b_str)
        if not string == "{}/{}".format(a, b):
            raise AssertionError
        new_string = "\\frac{" + str(a) + "}{" + str(b) + "}"
        return new_string
    except Exception:
        return string


def _remove_right_units(string: str) -> str:
    """Source: https://github.com/hendrycks/math
    Remove units (on the right).
    "\\text{ " only ever occurs (at least in the val set) when describing units.
    """
    if "\\text{ " in string:
        splits = string.split("\\text{ ")
        if not len(splits) == 2:
            raise AssertionError
        return splits[0]
    else:
        return string


def _fix_sqrt(string: str) -> str:
    """Source: https://github.com/hendrycks/math
    Reformat square roots.
    Example:
    >>> _fix_sqrt("\\sqrt3")
    \\sqrt{3}
    """
    if "\\sqrt" not in string:
        return string
    splits = string.split("\\sqrt")
    new_string = splits[0]
    for split in splits[1:]:
        if split[0] != "{":
            a = split[0]
            new_substr = "\\sqrt{" + a + "}" + split[1:]
        else:
            new_substr = "\\sqrt" + split
        new_string += new_substr
    return new_string


def _strip_string(string: str) -> str:
    """Source: https://github.com/hendrycks/math
    Apply the reformatting helper functions above.
    """
    # linebreaks
    string = string.replace("\n", "")
    # print(string)

    # remove inverse spaces
    string = string.replace("\\!", "")
    # print(string)

    # replace \\ with \
    string = string.replace("\\\\", "\\")
    # print(string)

    # replace tfrac and dfrac with frac
    string = string.replace("tfrac", "frac")
    string = string.replace("dfrac", "frac")
    # print(string)

    # remove \left and \right
    string = string.replace("\\left", "")
    string = string.replace("\\right", "")
    # print(string)

    # Remove circ (degrees)
    string = string.replace("^{\\circ}", "")
    string = string.replace("^\\circ", "")

    # remove dollar signs
    string = string.replace("\\$", "")

    # remove units (on the right)
    string = _remove_right_units(string)

    # remove percentage
    string = string.replace("\\%", "")
    string = string.replace("%", "")

    # " 0." equivalent to " ." and "{0." equivalent to "{." Alternatively, add "0" if "." is the start of the string
    string = string.replace(" .", " 0.")
    string = string.replace("{.", "{0.")
    # if empty, return empty string
    if len(string) == 0:
        return string
    if string[0] == ".":
        string = "0" + string

    # to consider: get rid of e.g. "k = " or "q = " at beginning
    if len(string.split("=")) == 2:
        if len(string.split("=")[0]) <= 2:
            string = string.split("=")[1]

    # fix sqrt3 --> sqrt{3}
    string = _fix_sqrt(string)

    # remove spaces
    string = string.replace(" ", "")

    # \frac1b or \frac12 --> \frac{1}{b} and \frac{1}{2}, etc.
    # Even works with \frac1{72} (but not \frac{72}1).
    # Also does a/b --> \\frac{a}{b}
    string = _fix_fracs(string)

    # manually change 0.5 --> \frac{1}{2}
    if string == "0.5":
        string = "\\frac{1}{2}"

    # NOTE: X/Y changed to \frac{X}{Y} in dataset, but in simple cases fix in case the model output is X/Y
    string = _fix_a_slash_b(string)

    return string


def get_answer(solution: Optional[str]) -> Optional[str]:
    if solution is None:
        return None
    last_boxed = last_boxed_only_string(solution)
    if last_boxed is None:
        return None
    answer = remove_boxed(last_boxed)
    if answer is None:
        return None
    return answer


def is_equiv(str1: Optional[str], str2: Optional[str]) -> float:
    """Returns (as a float) whether two strings containing math are equivalent up to differences of formatting in
    - units
    - fractions
    - square roots
    - superfluous LaTeX.
    Source: https://github.com/hendrycks/math
    """
    if str1 is None and str2 is None:
        print("WARNING: Both None")
        return 1.0
    if str1 is None or str2 is None:
        return 0.0

    try:
        ss1 = _strip_string(str1)
        ss2 = _strip_string(str2)
        return float(ss1 == ss2)
    except Exception:
        return float(str1 == str2)


def is_equiv_chain_of_thought(str1: str, str2: str) -> float:
    """Strips the solution first before calling `is_equiv`."""
    ans1 = get_answer(str1)
    ans2 = get_answer(str2)

    return is_equiv(ans1, ans2)


def voting_counts(responses):
    answers = {}
    for i in range(len(responses)):
        equiv = i
        if get_answer(responses[i]) is None:
            # ignore None answers
            continue
        for j in answers:
            if is_equiv_chain_of_thought(responses[i], responses[j]):
                equiv = j
                break
        if equiv in answers:
            answers[equiv] += 1
        else:
            answers[equiv] = 1
    return answers


def eval_math_responses(responses, solution=None, **args):
    """Select a response for a math problem using voting, and check if the response is correct if the solution is provided.

    Args:
        responses (list): The list of responses.
        solution (str): The canonical solution.

    Returns:
        dict: The success metrics.
    """
    n = len(responses)
    if not n:
        return {
            "expected_success": 0,
            "success": False,
            "success_vote": 0,
            "voted_answer": None,
            "votes": 0,
        }
    success_list = []
    if solution is not None:
        for i in range(n):
            response = responses[i]
            succeed = is_equiv_chain_of_thought(response, solution)
            success_list.append(succeed)
    # voting
    answers = voting_counts(responses)
    # find the answer with highest votes in answers
    answer, votes = max(answers.items(), key=lambda x: x[1], default=(0, 0))
    # check if the answer is correct
    success_vote = is_equiv_chain_of_thought(responses[answer], solution)
    return {
        "expected_success": 1 - pow(1 - sum(success_list) / n, n),
        "success": any(s for s in success_list),
        "success_vote": success_vote,
        "voted_answer": responses[answer],
        "votes": votes,
    }