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This logic is largely copied from the Hendrycks' MATH release (math_equivalence).
This file is adapted from OpenAI's PRM800K repository:
https://github.com/openai/prm800k/blob/main/prm800k/grading/math_normalize.py
Original License:
MIT License
Copyright (c) 2023 OpenAI
Permission is hereby granted, free of charge, to any person obtaining a copy
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.
"""
# flake8: noqa
import re
from typing import Optional
def normalize_answer(answer: Optional[str]) -> Optional[str]:
if answer is None:
return None
answer = answer.strip()
try:
# Remove enclosing `\text{}`.
m = re.search('^\\\\text\{(?P<text>.+?)\}$', answer)
if m is not None:
answer = m.group('text').strip()
return _strip_string(answer)
except:
return answer
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 substr[0] == '{':
new_str += substr
else:
try:
assert len(substr) >= 2
except:
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:
a = int(a)
b = int(b)
assert string == '{}/{}'.format(a, b)
new_string = '\\frac{' + str(a) + '}{' + str(b) + '}'
return new_string
except:
return string
def _remove_right_units(string):
# "\\text{ " only ever occurs (at least in the val set) when describing units
if '\\text{ ' in string:
splits = string.split('\\text{ ')
assert len(splits) == 2
return splits[0]
else:
return string
def _fix_sqrt(string):
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):
# 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
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