math_utils/grader.py

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# Copyright (c) 2023 OpenAI
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# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:

# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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# SOFTWARE.

# Copyright (c) 2021 Dan Hendrycks
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# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.


"""
This logic is largely copied from the Hendrycks' MATH release (math_equivalence), and borrowed from:
- https://github.com/microsoft/ToRA/blob/main/src/eval/grader.py
- https://github.com/microsoft/ProphetNet/tree/master/CRITIC
- https://github.com/openai/prm800k
"""


import contextlib
import re
import signal
import math
from math import isclose
from typing import Union

import sympy
from sympy import N, simplify
from sympy.parsing.latex import parse_latex
from sympy.parsing.sympy_parser import parse_expr


def is_digit(s):
    try:
        if "{,}" in str(s):
            num = float(str(s).replace("{,}", ""))
            return True, num

        num = float(str(s).replace(",", ""))
        return True, num
    except ValueError:
        return False, None


def normalize(answer, pi) -> str:
    # checking if answer is $<number> and removing $ in that case to compare
    if isinstance(answer, str) and bool(re.match(r'\$\d+(\.\d+)?', answer)):
        return answer[1:]

    # checking if answer is <number>% or <number>\\% and removing %
    if isinstance(answer, str) and (
        bool(re.match(r'^\d+(\.\d+)?%$', answer)) or bool(re.match(r'^\d+(\.\d+)?\\%$', answer))
    ):
        return answer.replace("\\%", "").replace("%", "")
    
    # handle base
    answer = handle_base(answer)

    # handle pi
    answer = handle_pi(answer, pi)

    return answer

def handle_base(x) -> str:
    if isinstance(x, str) and "_" in x:
        # Due to base
        x = x.split("_")[0]
        x = float(x)
        return int(x)
    return x


def handle_pi(string, pi):

    if isinstance(string, str) and "\pi" in string:
        # Find the first occurrence of "\pi"
        idx = string.find("\pi")

        # Iterate over the string and find all occurrences of "\pi" with a valid previous character
        while idx != -1:

            if idx > 0 and string[idx-1].isdigit():
                # Replace "\pi" with "*math.pi" if the previous character is a digit
                string = string[:idx] + f"*{pi}" + string[idx+3:]
            else:
                # Replace "\pi" with "1*math.pi" if the previous character is not a digit
                string = string[:idx] + f"1*{pi}" + string[idx+3:]

            # Find the next occurrence of "\pi"
            idx = string.find("\pi", idx + 1)

        # Evaluate the expression using eval() function
        try:
            string = eval(string)
        except:
            pass
            
    return string

def math_equal(
    prediction: Union[bool, float, str],
    reference: Union[float, str],
    include_percentage: bool = True,
    tolerance: float = 1e-4,
    timeout: float = 10.0,
    pi: float = math.pi
) -> bool:
    """
    Exact match of math if and only if:
    1. numerical equal: both can convert to float and are equal
    2. symbolic equal: both can convert to sympy expression and are equal
    """

    prediction = normalize(prediction, pi)
    reference = normalize(reference, pi)

    if isinstance(prediction, str) and len(prediction) > 1000:  # handling weird corner-cases
        prediction = prediction[:1000]

    # 0. string comparison
    if isinstance(prediction, str) and isinstance(reference, str):
        if prediction.strip().lower() == reference.strip().lower():
            return True
        if prediction.replace(" ", "") == reference.replace(" ", ""):
            return True

    try:  # 1. numerical equal
        if is_digit(prediction)[0] and is_digit(reference)[0]:
            prediction = is_digit(prediction)[1]
            reference = is_digit(reference)[1]
            # number questions
            if include_percentage:
                gt_result = [reference / 100, reference, reference * 100]
            else:
                gt_result = [reference]
            for item in gt_result:
                try:
                    if isclose(item, prediction, rel_tol=tolerance):
                        return True
                except Exception:
                    continue
            return False
    except Exception:
        pass

    if not prediction and prediction not in [0, False]:
        return False

    # 2. symbolic equal
    reference = str(reference).strip()
    prediction = str(prediction).strip()

    ## deal with [], (), {}
    prediction = format_intervals(prediction)

    pred_str, ref_str = prediction, reference
    if (prediction.startswith("[") and prediction.endswith("]") and not reference.startswith("(")) or (
        prediction.startswith("(") and prediction.endswith(")") and not reference.startswith("[")
    ):
        pred_str = pred_str.strip("[]()")
        ref_str = ref_str.strip("[]()")
    for s in ["{", "}", "(", ")"]:
        ref_str = ref_str.replace(s, "")
        pred_str = pred_str.replace(s, "")
    if pred_str == ref_str:
        return True

    ## [a, b] vs. [c, d], return a==c and b==d
    if (
        prediction
        and reference
        and prediction[0] in "(["
        and prediction[-1] in ")]"
        and prediction[0] == reference[0]
        and prediction[-1] == reference[-1]
    ):
        pred_parts = prediction[1:-1].split(",")
        ref_parts = reference[1:-1].split(",")
        if len(pred_parts) == len(ref_parts):
            if all(
                [
                    math_equal(pred_pt, ref_pt, include_percentage, tolerance)
                    for pred_pt, ref_pt in zip(pred_parts, ref_parts)
                ]
            ):
                return True

    if "," in prediction and "," in reference:
        pred_parts = [item.strip() for item in prediction.split(",")]
        ref_parts = [item.strip() for item in reference.split(",")]

        if len(pred_parts) == len(ref_parts):
            if all(
                [
                    math_equal(pred_parts[i], ref_parts[i], include_percentage, tolerance)
                    for i in range(len(pred_parts))
                ]
            ):
                return True
            else:
                return False

    # if we have point == tuple of values
    if prediction.startswith("Point") and reference[0] == "(" and reference[-1] == ")":
        pred_parts = prediction[prediction.find("(") + 1 : -1].split(",")
        ref_parts = reference[1:-1].split(",")
        if len(pred_parts) == len(ref_parts):
            if all(
                [
                    math_equal(pred_pt, ref_pt, include_percentage, tolerance)
                    for pred_pt, ref_pt in zip(pred_parts, ref_parts)
                ]
            ):
                return True

    # if reference is a matrix
    if "\begin{pmatrix}" in reference and prediction.startswith("Matrix"):
        try:
            pred_matrix = parse_expr(prediction)
            ref_matrix_items = reference.split()[1:-1:2]
            if len(pred_matrix) == len(ref_matrix_items):
                if all(
                    [
                        math_equal(pred, ref, include_percentage, tolerance)
                        for ref, pred in zip(ref_matrix_items, pred_matrix)
                    ]
                ):
                    return True
        except Exception:
            pass
    elif "\begin{pmatrix}" in reference and prediction.startswith("[") and prediction.endswith("]"):
        if isinstance(eval(prediction), list):
            try:
                pred_matrix = eval(prediction)
                # ref_matrix_items = reference.split()[1:-1:2]
                ref_matrix_items = reference.lstrip("\\begin{pmatrix}").lstrip("\begin{pmatrix}").rstrip("\\end{pmatrix}").rstrip("\end{pmatrix}")
                ref_matrix_items = ref_matrix_items.split("\\")
                ref_matrix_items = [row.split("&") if "&" in row else row for row in ref_matrix_items]
                if len(pred_matrix) == len(ref_matrix_items):
                    if all(
                        [
                            math_equal(pred, ref, include_percentage, tolerance)
                            for ref, pred in zip(ref_matrix_items, pred_matrix)
                        ]
                    ):
                        return True
            except Exception:
                pass

    return symbolic_equal(prediction, reference, tolerance, timeout)


def symbolic_equal(a, b, tolerance, timeout=10.0):
    def _parse(s):
        for f in [parse_expr, parse_latex]:
            try:
                with time_limit(timeout):
                    return f(s)
            except Exception:
                pass
        return s

    a = _parse(a)
    b = _parse(b)

    try:
        with time_limit(timeout):
            if simplify(a - b) == 0:
                return True
    except Exception:
        pass

    try:
        with time_limit(timeout):
            if isclose(N(a), N(b), rel_tol=tolerance):
                return True
    except Exception:
        pass
    return False


def extract_answer(string):
    """Extract Answer String from \\boxed expression."""
    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]

    if retval:
        left = "\\boxed{"
        try:
            assert retval[: len(left)] == left
            assert retval[-1] == "}"
            return retval[len(left) : -1]
        except AssertionError:
            return None

    return None


class TimeoutException(Exception):
    pass


@contextlib.contextmanager
def time_limit(seconds: float):
    def signal_handler(signum, frame):
        raise TimeoutException("Timed out!")

    signal.setitimer(signal.ITIMER_REAL, seconds)
    signal.signal(signal.SIGALRM, signal_handler)
    try:
        yield
    finally:
        signal.setitimer(signal.ITIMER_REAL, 0)


def format_intervals(prediction):
    patterns = {
        "Interval(": r"^Interval\((.*)\)$",
        "Interval.Ropen(": r"^Interval\.Ropen\((.*)\)$",
        "Interval.Lopen(": r"^Interval\.Lopen\((.*)\)$",
        "Interval.open(": r"^Interval\.open\((.*)\)$",
    }

    for key, pattern in patterns.items():
        match = re.match(pattern, prediction)
        if match:
            inner_content = match.group(1)

            if key == "Interval(":  # Intarval(a, b) == [a, b]
                return f"[{inner_content}]"
            elif key == "Interval.Ropen(":  # Intarval.Ropen(a, b) == [a, b)
                return f"[{inner_content})"
            elif key == "Interval.Lopen(":  # Intarval.Lopen(a, b) == (a, b]
                return f"({inner_content}]"
            elif key == "Interval.open(":  # Intarval.open(a, b) == (a, b)
                return f"({inner_content})"

    return prediction


def _test_math_equal():
    ref = "6,-2"
    pred = "6"
    print(math_equal(ref, pred))

def _test_math_equal():
    pi = math.pi
    ref = "900\pi"
    pred = 812.0
    print(math_equal(pred, ref, pi=pi))

    ref = "25\pi"
    pred = 78.5
    print(math_equal(pred, ref, pi=pi))

    ref = "90\pi"
    pred = 282.6
    print(math_equal(pred, ref, pi=pi))

    ref = "24+4\pi"
    pred = 36.57142857142857
    print(math_equal(pred, ref, pi=pi))

    ref = "9\pi"
    pred = 28.274309999999993
    print(math_equal(pred, ref, pi=pi))


def _test_math_equal():
    ref = "\\begin{pmatrix}0&1\\1&0\end{pmatrix}"
    # ref=ref.split()[1:-1:2]
    pred = [[0,1], [1,0]]
    print(math_equal(pred, ref))

if __name__ == "__main__":
    _test_math_equal()