Blame for src/elbench/judges/math_rule/math_parser.py

"""
The logic in this file largely borrows from Qwen2.5-Math codebase at https://github.com/QwenLM/Qwen2.5-Math:
"""
# flake8: noqa
import re
import regex
from latex2sympy2_extended import latex2sympy
from math import isclose
from sympy import N, simplify
from sympy.parsing.latex import parse_latex
from sympy.parsing.sympy_parser import parse_expr
from word2number import w2n


def convert_word_number(text: str) -> str:
    try:
        text = str(w2n.word_to_num(text))
    except Exception:
        pass
    return text


def _fix_fracs(string):
    substrs = string.split('\\frac')
    new_str = substrs[0]
    if len(substrs) > 1:
        substrs = substrs[1:]
        for substr in substrs:
            new_str += '\\frac'
            if len(substr) > 0 and substr[0] == '{':
                new_str += substr
            else:
                try:
                    assert len(substr) >= 2
                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):
    if len(string.split('/')) != 2:
        return string
    a = string.split('/')[0]
    b = string.split('/')[1]
    try:
        if 'sqrt' not in a:
            a = int(a)
        if 'sqrt' not in b:
            b = int(b)
        assert string == '{}/{}'.format(a, b)
        new_string = '\\frac{' + str(a) + '}{' + str(b) + '}'
        return new_string
    except Exception:
        return string


def _fix_sqrt(string):
    _string = re.sub(r'\\sqrt(\w+)', r'\\sqrt{\1}', string)
    return _string


def strip_answer_string(string):
    string = str(string).strip()
    # linebreaks
    string = string.replace('\n', '')

    # right "."
    string = string.rstrip('.')

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

    # matrix
    string = re.sub(r'\\begin\{array\}\{.*?\}', r'\\begin{pmatrix}', string)
    string = re.sub(r'\\end\{array\}', r'\\end{pmatrix}', string)
    string = string.replace('bmatrix', 'pmatrix')

    # replace tfrac and dfrac with frac
    string = string.replace('tfrac', 'frac')
    string = string.replace('dfrac', 'frac')
    string = (string.replace('\\neq', '\\ne').replace('\\leq', '\\le').replace('\\geq', '\\ge'))

    # remove \left and \right
    string = string.replace('\\left', '')
    string = string.replace('\\right', '')
    string = string.replace('\\{', '{')
    string = string.replace('\\}', '}')

    # Function to replace number words with corresponding digits
    def replace_match(match):
        word = match.group(1).lower()
        if convert_word_number(word) == word:
            return match.group(0)
        else:
            return convert_word_number(word)

    string = re.sub(r'\\text\{([a-zA-Z]+)\}', replace_match, string)

    # Before removing unit, check if the unit is squared (for surface area)
    string = re.sub(r'(cm|inches)\}\^2', r'\1}', string)

    # Remove unit: miles, dollars if after is not none
    _string = re.sub(r'\\text{.*?}$', '', string).strip()
    if _string != '' and _string != string:
        # print("Warning: unit not removed: '{}' -> '{}'".format(string, _string))
        string = _string

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

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

    # convert word number to digit
    string = convert_word_number(string)

    # replace "\\text{...}" to "..."
    string = re.sub(r'\\text\{(.*?)\}', r'\1', string)
    for key in ['x=', 'y=', 'z=', 'x\\in', 'y\\in', 'z\\in', 'x\\to', 'y\\to', 'z\\to']:
        string = string.replace(key, '')
    string = string.replace('\\emptyset', r'{}')
    string = string.replace('(-\\infty,\\infty)', '\\mathbb{R}')

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

    # cdot
    # string = string.replace("\\cdot", "")
    if (
        string.startswith('{') and string.endswith('}') and string.isalnum()
        or string.startswith('(') and string.endswith(')') and string.isalnum()
        or string.startswith('[') and string.endswith(']') and string.isalnum()
    ):
        string = string[1:-1]

    # inf
    string = string.replace('infinity', '\\infty')
    if '\\infty' not in string:
        string = string.replace('inf', '\\infty')
    string = string.replace('+\\inity', '\\infty')

    # and
    string = string.replace('and', '')
    string = string.replace('\\mathbf', '')

    # use regex to remove \mbox{...}
    string = re.sub(r'\\mbox{.*?}', '', string)

    # quote
    string.replace("'", '')
    string.replace('"', '')

    # i, j
    if 'j' in string and 'i' not in string:
        string = string.replace('j', 'i')

    # replace a.000b where b is not number or b is end, with ab, use regex
    string = re.sub(r'(\d+)\.0*([^\d])', r'\1\2', string)
    string = re.sub(r'(\d+)\.0*$', r'\1', string)

    # 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]

    string = _fix_sqrt(string)
    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)

    # 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)

    # Remove unnecessary '\' before integers
    string = re.sub(r'\\(?=\-?\d+(\\|\)|,|\]|$))', '', string)

    # Remove grade level (e.g., 12th grade) and just maintain the integer
    string = re.sub(r'thgrade$', '', string)

    # Normalize thousands-formatted numbers (e.g., 70,000 or -1,234,567.89) by removing commas
    # This must run before the "list of integers" sorting to avoid misclassifying numbers with thousand separators.
    if re.fullmatch(r'\s*-?\d{1,3}(?:,\d{3})+(?:\.\d+)?\s*', string):
        string = string.replace(',', '')

    # If the answer is a list of integers (without parenthesis), sort them
    if re.fullmatch(r'(\s*-?\d+\s*,)*\s*-?\d+\s*', string):
        # Split the string into a list of integers
        try:
            integer_list = list(map(int, string.split(',')))
        except Exception:
            integer_list = list(map(int, '-1,-1'.split(',')))

        # Sort the list in ascending order
        sorted_list = sorted(integer_list)

        # Join the sorted list back into a comma-separated string
        string = ','.join(map(str, sorted_list))

    return string


def extract_answer(pred_str, use_last_number=True):
    pred_str = pred_str.replace('\u043a\u0438', '')
    if 'final answer is $' in pred_str and '$. I hope' in pred_str:
        # minerva_math
        tmp = pred_str.split('final answer is $', 1)[1]
        pred = tmp.split('$. I hope', 1)[0].strip()
    elif 'boxed' in pred_str:
        ans = pred_str.split('boxed')[-1]
        if len(ans) == 0:
            return ''
        elif ans[0] == '{':
            stack = 1
            a = ''
            for c in ans[1:]:
                if c == '{':
                    stack += 1
                    a += c
                elif c == '}':
                    stack -= 1
                    if stack == 0:
                        break
                    a += c
                else:
                    a += c
        else:
            a = ans.split('$')[0].strip()
        pred = a
    elif 'he answer is' in pred_str:
        pred = pred_str.split('he answer is')[-1].strip()
    elif 'final answer is' in pred_str:
        pred = pred_str.split('final answer is')[-1].strip()
    elif '答案是' in pred_str:
        # Handle Chinese few-shot multiple choice problem answer extraction
        pred = pred_str.split('答案是')[1].strip().split('\n\n')[0].strip()
    elif 'ANSWER:' in pred_str:
        pred = pred_str.split('ANSWER:')[-1].strip()
    else:  # use the last number
        if use_last_number:
            pattern = '-?\d*\.?\d+'
            pred = re.findall(pattern, pred_str.replace(',', ''))
            if len(pred) >= 1:
                pred = pred[-1]
            else:
                pred = ''
        else:
            pred = ''

    # multiple line
    # pred = pred.split("\n")[0]
    pred = re.sub(r'\n\s*', '', pred)
    if pred != '' and pred[0] == ':':
        pred = pred[1:]
    if pred != '' and pred[-1] == '.':
        pred = pred[:-1]
    if pred != '' and pred[-1] == '/':
        pred = pred[:-1]
    pred = strip_answer_string(pred)
    return pred


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 Exception:
        if num.endswith('%'):
            num = num[:-1]
            if num.endswith('\\'):
                num = num[:-1]
            try:
                return float(num) / 100
            except Exception:
                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,
    reference,
    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
    """
    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 Exception:
        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 'pmatrix' not 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

    if symbolic_equal(prediction, reference):
        return True

    return False


def numeric_equal(prediction: float, reference: float):
    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 Exception:
                try:
                    return f(s)
                except Exception:
                    pass
        return s

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

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

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

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

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

    return False

def process_math500(prediction, ref_answer):
    return float(math_equal(prediction, ref_answer))

def main():
    prediction = r'''Here's a step-by-step solution:

1.  **Identify the given information from the diagram and problem statement:**
    *   Triangle DEF is a right-angled triangle, with the right angle at E (indicated by the right-angle mark).
    *   The length of side EF is 7 (from the label on the diagram and the coordinates E=(0,7), F=(0,0)).
    *   We are given $\sin D = 0.7$.

2.  **Recall the definition of sine in a right-angled triangle:**
    For an angle in a right-angled triangle, the sine is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
    In triangle DEF, for angle D:
    *   The side opposite to angle D is EF.
    *   The hypotenuse is DF.
    Therefore, $\sin D = \frac{EF}{DF}$.

3.  **Use the given $\sin D$ and EF to find the length of the hypotenuse DF:**
    We have $\sin D = 0.7$ and $EF = 7$.
    Substitute these values into the sine formula:
    $0.7 = \frac{7}{DF}$
    To solve for DF, multiply both sides by DF and then divide by 0.7:
    $DF = \frac{7}{0.7}$
    $DF = \frac{7}{\frac{7}{10}}$
    $DF = 7 \times \frac{10}{7}$
    $DF = 10$.

4.  **Use the Pythagorean theorem to find the length of DE:**
    Since triangle DEF is a right-angled triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (DF) is equal to the sum of the squares of the other two sides (DE and EF):
    $DE^2 + EF^2 = DF^2$
    Substitute the known values $EF = 7$ and $DF = 10$:
    $DE^2 + 7^2 = 10^2$
    $DE^2 + 49 = 100$

5.  **Solve for DE:**
    Subtract 49 from both sides:
    $DE^2 = 100 - 49$
    $DE^2 = 51$
    Take the square root of both sides:
    $DE = \sqrt{51}$

The final answer is $\boxed{\sqrt{51}}$.'''
    print(process_math500(extract_answer(prediction), '\\sqrt{51}'))

def main_units():

    print(math_equal('\n\\boxed{70,\\!000}\n', '70000'))
    print(extract_answer('The answer is \\boxed{70,\\!000}'))
    print(strip_answer_string(extract_answer('The answer is \\boxed{70,\\!000}')))
    print(math_equal(extract_answer('The answer is \\boxed{70,\\!000}'), '70000'))


if __name__ == '__main__':
    main()