AReaL/grader.py

"""This logic is largely copied from the Hendrycks' MATH release
(math_equivalence), and borrowed from:

- https://github.com/microsoft/ProphetNet/tree/master/CRITIC
- https://github.com/openai/prm800k
- https://github.com/microsoft/ToRA/blob/main/src/eval/grader.py
- https://github.com/deepseek-ai/DeepSeek-Math/blob/main/evaluation/eval/eval_utils.py
"""

import multiprocessing
import re
from collections import defaultdict
from math import isclose
from typing import Union

import regex
from latex2sympy2 import latex2sympy
from sympy import N, simplify
from sympy.parsing.latex import parse_latex
from sympy.parsing.sympy_parser import parse_expr

# from .parser import choice_answer_clean, strip_string
# from parser import choice_answer_clean


def choice_answer_clean(pred: str):
    pred = pred.strip("\n").rstrip(".").rstrip("/").strip(" ").lstrip(":")
    # Clean the answer based on the dataset
    tmp = re.findall(r"\b(A|B|C|D|E)\b", pred.upper())
    if tmp:
        pred = tmp
    else:
        pred = [pred.strip().strip(".")]
    pred = pred[-1]
    # Remove the period at the end, again!
    pred = pred.rstrip(".").rstrip("/")
    return pred


def parse_digits(num):
    num = regex.sub(",", "", str(num))
    try:
        return float(num)
    except:
        if num.endswith("%"):
            num = num[:-1]
            if num.endswith("\\"):
                num = num[:-1]
            try:
                return float(num) / 100
            except:
                pass
    return None


def is_digit(num):
    # paired with parse_digits
    return parse_digits(num) is not None


def str_to_pmatrix(input_str):
    input_str = input_str.strip()
    matrix_str = re.findall(r"\{.*,.*\}", input_str)
    pmatrix_list = []

    for m in matrix_str:
        m = m.strip("{}")
        pmatrix = r"\begin{pmatrix}" + m.replace(",", "\\") + r"\end{pmatrix}"
        pmatrix_list.append(pmatrix)

    return ", ".join(pmatrix_list)


def math_equal(
    prediction: Union[bool, float, str],
    reference: Union[float, str],
    include_percentage: bool = True,
    is_close: bool = True,
    timeout: bool = False,
) -> 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
    """
    # print("Judge:", prediction, reference)
    if prediction is None or reference is None:
        return False
    if str(prediction.strip().lower()) == str(reference.strip().lower()):
        return True
    if (
        reference in ["A", "B", "C", "D", "E"]
        and choice_answer_clean(prediction) == reference
    ):
        return True

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

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

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

    ## pmatrix (amps)
    if "pmatrix" in prediction and not "pmatrix" in reference:
        reference = str_to_pmatrix(reference)

    ## deal with [], (), {}
    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.lower() == ref_str.lower():
        return True

    ## [a, b] vs. [c, d], return a==c and b==d
    if (
        regex.match(r"(\(|\[).+(\)|\])", prediction) is not None
        and regex.match(r"(\(|\[).+(\)|\])", reference) is not None
    ):
        pred_parts = prediction[1:-1].split(",")
        ref_parts = reference[1:-1].split(",")
        if len(pred_parts) == len(ref_parts):
            if all(
                [
                    math_equal(
                        pred_parts[i], ref_parts[i], include_percentage, is_close
                    )
                    for i in range(len(pred_parts))
                ]
            ):
                return True
    if (
        (
            prediction.startswith("\\begin{pmatrix}")
            or prediction.startswith("\\begin{bmatrix}")
        )
        and (
            prediction.endswith("\\end{pmatrix}")
            or prediction.endswith("\\end{bmatrix}")
        )
        and (
            reference.startswith("\\begin{pmatrix}")
            or reference.startswith("\\begin{bmatrix}")
        )
        and (
            reference.endswith("\\end{pmatrix}") or reference.endswith("\\end{bmatrix}")
        )
    ):
        pred_lines = [
            line.strip()
            for line in prediction[
                len("\\begin{pmatrix}") : -len("\\end{pmatrix}")
            ].split("\\\\")
            if line.strip()
        ]
        ref_lines = [
            line.strip()
            for line in reference[
                len("\\begin{pmatrix}") : -len("\\end{pmatrix}")
            ].split("\\\\")
            if line.strip()
        ]
        matched = True
        if len(pred_lines) == len(ref_lines):
            for pred_line, ref_line in zip(pred_lines, ref_lines):
                pred_parts = pred_line.split("&")
                ref_parts = ref_line.split("&")
                if len(pred_parts) == len(ref_parts):
                    if not all(
                        [
                            math_equal(
                                pred_parts[i],
                                ref_parts[i],
                                include_percentage,
                                is_close,
                            )
                            for i in range(len(pred_parts))
                        ]
                    ):
                        matched = False
                        break
                else:
                    matched = False
                if not matched:
                    break
        else:
            matched = False
        if matched:
            return True

    if prediction.count("=") == 1 and reference.count("=") == 1:
        pred = prediction.split("=")
        pred = f"{pred[0].strip()} - ({pred[1].strip()})"
        ref = reference.split("=")
        ref = f"{ref[0].strip()} - ({ref[1].strip()})"
        if symbolic_equal(pred, ref) or symbolic_equal(f"-({pred})", ref):
            return True
    elif (
        prediction.count("=") == 1
        and len(prediction.split("=")[0].strip()) <= 2
        and "=" not in reference
    ):
        if math_equal(
            prediction.split("=")[1], reference, include_percentage, is_close
        ):
            return True
    elif (
        reference.count("=") == 1
        and len(reference.split("=")[0].strip()) <= 2
        and "=" not in prediction
    ):
        if math_equal(
            prediction, reference.split("=")[1], include_percentage, is_close
        ):
            return True

    # symbolic equal with sympy
    if timeout:
        if call_with_timeout(symbolic_equal_process, prediction, reference):
            return True
    else:
        if symbolic_equal(prediction, reference):
            return True

    return False


def math_equal_process(param):
    return math_equal(param[-2], param[-1])


def numeric_equal(prediction: float, reference: float):
    # Note that relative tolerance has significant impact
    # on the result of the synthesized GSM-Hard dataset
    # if reference.is_integer():
    #     return isclose(reference, round(prediction), abs_tol=1e-4)
    # else:
    # prediction = round(prediction, len(str(reference).split(".")[-1]))
    return isclose(reference, prediction, rel_tol=1e-4)


def symbolic_equal(a, b):
    def _parse(s):
        for f in [parse_latex, parse_expr, latex2sympy]:
            try:
                return f(s.replace("\\\\", "\\"))
            except:
                try:
                    return f(s)
                except:
                    pass
        return s

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

    # direct equal
    try:
        if str(a) == str(b) or a == b:
            return True
    except:
        pass

    # simplify equal
    try:
        if a.equals(b) or simplify(a - b) == 0:
            return True
    except:
        pass

    # equation equal
    try:
        if (abs(a.lhs - a.rhs)).equals(abs(b.lhs - b.rhs)):
            return True
    except:
        pass

    try:
        if numeric_equal(float(N(a)), float(N(b))):
            return True
    except:
        pass

    # matrix
    try:
        # if a and b are matrix
        if a.shape == b.shape:
            _a = a.applyfunc(lambda x: round(x, 3))
            _b = b.applyfunc(lambda x: round(x, 3))
            if _a.equals(_b):
                return True
    except:
        pass

    return False


def symbolic_equal_process(a, b, output_queue):
    result = symbolic_equal(a, b)
    output_queue.put(result)


def call_with_timeout(func, *args, timeout=3, **kwargs):
    output_queue = multiprocessing.Queue()
    process_args = args + (output_queue,)
    process = multiprocessing.Process(target=func, args=process_args, kwargs=kwargs)
    process.start()
    process.join(timeout)

    if process.is_alive():
        process.terminate()
        process.join()
        return False

    return output_queue.get()


def _test_math_equal():
    # print(math_equal("0.0833333333333333", "\\frac{1}{12}"))
    # print(math_equal("(1,4.5)", "(1,\\frac{9}{2})"))
    # print(math_equal("\\frac{x}{7}+\\frac{2}{7}", "\\frac{x+2}{7}", timeout=True))
    # print(math_equal("\\sec^2(y)", "\\tan^2(y)+1", timeout=True))
    # print(math_equal("\\begin{pmatrix}-\\frac{7}{4}&-2\\\\4&\\frac{1}{4}\\end{pmatrix}", "(\\begin{pmatrix}-\\frac{7}{4}&-2\\\\4&\\frac{1}{4}\\\\\\end{pmatrix})", timeout=True))

    # pred = '\\begin{pmatrix}\\frac{1}{3x^{2/3}}&0&0\\\\0&1&0\\\\-\\sin(x)&0&0\\end{pmatrix}'
    # gt = '(\\begin{pmatrix}\\frac{1}{3\\sqrt[3]{x}^2}&0&0\\\\0&1&0\\\\-\\sin(x)&0&0\\\\\\end{pmatrix})'

    # pred= '-\\frac{8x^2}{9(x^2-2)^{5/3}}+\\frac{2}{3(x^2-2)^{2/3}}'
    # gt= '-\\frac{2(x^2+6)}{9(x^2-2)\\sqrt[3]{x^2-2}^2}'

    # pred =  '-34x-45y+20z-100=0'
    # gt = '34x+45y-20z+100=0'

    # pred = '\\frac{100}{3}'
    # gt = '33.3'

    # pred = '\\begin{pmatrix}0.290243531202435\\\\0.196008371385084\\\\-0.186381278538813\\end{pmatrix}'
    # gt = '(\\begin{pmatrix}0.29\\\\0.196\\\\-0.186\\\\\\end{pmatrix})'

    # pred = '\\frac{\\sqrt{\\sqrt{11}+\\sqrt{194}}}{2\\sqrt{33}+15}'
    # gt = '\\frac{\\sqrt{\\sqrt{11}+\\sqrt{194}}}{15+2\\sqrt{33}}'

    # pred = '(+5)(b+2)'
    # gt = '(a+5)(b+2)'

    # pred = '\\frac{1+\\sqrt{5}}{2}'
    # gt = '2'

    # pred = '\\frac{34}{16}+\\frac{\\sqrt{1358}}{16}', gt = '4'
    # pred = '1', gt = '1\\\\sqrt{19}'

    # pred = "(0.6,2.6667]"
    # gt = "(\\frac{3}{5},\\frac{8}{3}]"

    gt = "x+0.5+0.5"
    pred = "x+1"

    print(math_equal(pred, gt, timeout=True))


if __name__ == "__main__":
    _test_math_equal()