146 lines
4.2 KiB
Python
146 lines
4.2 KiB
Python
"""Optional sympy-based math grader (adapted from OpenAI PRM800K, MIT license).
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Imported lazily by the math_equal scorer; only needed when normalized string
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equality is not enough (unreduced fractions, symbolic forms, units).
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Requires: pip install sympy pylatexenc
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"""
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import logging
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from typing import Optional
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logger = logging.getLogger(__name__)
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try:
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import sympy
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from pylatexenc import latex2text
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from sympy.parsing import sympy_parser
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_OK = True
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except ImportError: # pragma: no cover - optional dependency
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_OK = False
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BAD_SUBSTRINGS = ('^{', '^(')
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TUPLE_CHARS = '()[]'
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def _sympy_parse(expr: str):
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return sympy_parser.parse_expr(
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expr.replace('^', '**'),
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transformations=(
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sympy_parser.standard_transformations
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+ (sympy_parser.implicit_multiplication_application,)
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),
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)
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def _parse_latex(expr: str) -> str:
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expr = expr.replace('\\tfrac', '\\frac').replace('\\dfrac', '\\frac')
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expr = latex2text.LatexNodes2Text().latex_to_text(expr)
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return (expr.replace('√', 'sqrt').replace('π', 'pi').replace('·', '*')
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.replace('×', '*').strip())
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def _strip_commas(expr: str) -> str:
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import re
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return re.sub(r'(\d),(\d\d\d)(?=\D|$)', r'\1\2', expr)
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def _is_float(x) -> bool:
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try:
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float(x)
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return True
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except (TypeError, ValueError):
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return False
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def _str_is_int(x: str) -> bool:
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try:
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return abs(float(x) - int(round(float(x)))) <= 1e-7
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except (TypeError, ValueError):
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return False
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def _is_frac(expr: str) -> bool:
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import re
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return bool(re.fullmatch(r'-?[0-9]+.?/0*[1-9][0-9]*.?', expr or ''))
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def _normalize(expr: Optional[str]) -> Optional[str]:
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import re
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if expr is None:
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return None
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m = re.fullmatch(r'\\text\{(.+?)\}', expr)
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if m:
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expr = m.group(1)
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expr = (expr.replace('\\%', '%').replace('\\$', '$').replace('$', '').replace('%', '')
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.replace(' or ', ' , ').replace(' and ', ' , ')
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.replace('million', '*10^6').replace('billion', '*10^9'))
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for unit in ('degree', 'cm', 'meter', 'mile', 'second', 'minute', 'hour',
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'day', 'week', 'month', 'year', 'foot', 'feet', 'inch', 'yard'):
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expr = re.sub(unit + r'(es)?(s)? *(\^[0-9]+)?', '', expr)
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expr = re.sub(r'\^ *\\circ', '', expr)
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if len(expr) > 1 and expr[0] == '{' and expr[-1] == '}':
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expr = expr[1:-1]
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expr = _strip_commas(expr)
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if _is_float(expr):
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try:
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f = float(expr)
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if abs(f - round(f)) <= 1e-7:
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expr = str(int(round(f)))
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except (TypeError, ValueError):
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pass
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if '\\' in expr:
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try:
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expr = _parse_latex(expr)
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except Exception:
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pass
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expr = re.sub(r'- *', '-', expr.replace(' ', ''))
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expr = expr.replace('{', '').replace('}', '').lower()
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if _str_is_int(expr):
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expr = str(int(round(float(expr))))
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return expr
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def _split_tuple(expr: str):
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expr = _strip_commas(expr)
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if (len(expr) > 2 and expr[0] in TUPLE_CHARS and expr[-1] in TUPLE_CHARS
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and all(c not in expr[1:-1] for c in TUPLE_CHARS)):
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return [e.strip() for e in expr[1:-1].split(',')]
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return [expr]
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def _sympy_equal(a: str, b: str) -> bool:
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try:
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diff = _sympy_parse(f'({a})-({b})')
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return sympy.simplify(diff) == 0
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except Exception:
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return False
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def grade_answer(given_answer: str, ground_truth: str) -> bool:
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"""True iff equal under normalization or sympy simplification."""
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if not _OK:
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raise ImportError('pip install sympy pylatexenc for symbolic math grading')
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if given_answer is None:
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return False
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a, b = _normalize(given_answer), _normalize(ground_truth)
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if a == b:
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return True
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if not a or not b:
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return False
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a_elems, b_elems = _split_tuple(a), _split_tuple(b)
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if len(a_elems) != len(b_elems):
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return False
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for x, y in zip(a_elems, b_elems):
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if _is_frac(x) and _is_frac(y):
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if x != y:
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return False
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elif _str_is_int(x) != _str_is_int(y):
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return False
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elif not _sympy_equal(x, y):
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return False
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return True
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