Update Dockerfile, eval_gsm8k.py, eval_math.py, LICENSE, read.md, README.MD,...

Update Dockerfile, eval_gsm8k.py, eval_math.py, LICENSE, read.md, README.MD, requirements.txt, run_mistral.sh, run.sh, util.py, train_math.py, imgs/dcu.png, imgs/metamath.svg, data/README.md, data/test/MATH_test.jsonl, data/test/GSM8K_test.jsonl, data/test/GSM8K_Backward.jsonl, data/train/README.md, code_for_generating_data/ReadMe.md, code_for_generating_data/code/main_backward_reasoning.py, code_for_generating_data/code/main_forward_reasoning.py, code_for_generating_data/code/main_create_backward_questions.py, code_for_generating_data/code/main_rephrase_question.py, code_for_generating_data/code/path_init.py, code_for_generating_data/code/main_self_verification.py, code_for_generating_data/code/run_create_backward_questions.sh, code_for_generating_data/code/run_forward.sh, code_for_generating_data/code/run_backward.sh, code_for_generating_data/code/run_sv.sh, code_for_generating_data/code/run_rephrase.sh, code_for_generating_data/code/utils/__init__.py, code_for_generating_data/code/utils/answer_clean_utils.py, code_for_generating_data/code/utils/config_utils.py, code_for_generating_data/code/utils/log_utils.py, code_for_generating_data/code/utils/math_utils.py, code_for_generating_data/code/utils/openai_api_utils.py, code_for_generating_data/code/utils/parallel_utils.py, code_for_generating_data/code/utils/time_utils.py, code_for_generating_data/code/utils/path_utils.py, code_for_generating_data/configs/ansaug_cot_math.txt, code_for_generating_data/configs/ansaug_cot_gsm8k.txt, code_for_generating_data/configs/fobar_cot_gsm8k.txt, code_for_generating_data/configs/fobar_cot_math.txt, code_for_generating_data/configs/rephrase_cot_gsm8k.txt, code_for_generating_data/configs/rephrase_cot_math.txt, code_for_generating_data/configs/sv_cot_gsm8k.txt, code_for_generating_data/configs/sv_cot_math.txt, code_for_generating_data/configs/sv_rewrite_question_prompt_gsm8k.txt, code_for_generating_data/configs/sv_rewrite_question_prompt_math.txt, code_for_generating_data/data/gsm8k_train.json, code_for_generating_data/data/MATH_train.json files

code_for_generating_data/code/utils/openai_api_utils.py

+import openai
+import time
+import os
+
+
+openai.api_key = os.environ["APIKEY"]
+# openai.organization = ""
+
+
+def create_response(prompt_input, eng='text-davinci-002', max_tokens=1024, temperature=0.0, stop="Q", timeout=20):
+    assert eng in ('text-davinci-002', 'text-davinci-003')
+    response = openai.Completion.create(
+        engine=eng,
+        prompt=prompt_input,
+        temperature=temperature,
+        max_tokens=max_tokens,
+        top_p=1,
+        frequency_penalty=0.0,
+        presence_penalty=0.0,
+        stop=["{}:".format(stop)],
+        request_timeout=timeout
+    )
+    return response
+
+
+def create_response_chat(prompt_input, eng='gpt-3.5-turbo',  temperature=0.0, timeout=20):
+    assert eng in ["gpt-3.5-turbo", "gpt-3.5-turbo-16k", "gpt-3.5-turbo-0613", "gpt-3.5-turbo-16k-0613",
+               "gpt-4", "gpt-4-0613", "gpt-4-32k", "gpt-4-32k-0613", "gpt-3.5-turbo-1106"]
+    response = openai.ChatCompletion.create(
+        model=eng,
+        messages=prompt_input,
+        temperature=temperature,
+        request_timeout=timeout,
+    )
+    return response
\ No newline at end of file

code_for_generating_data/code/utils/parallel_utils.py

+import time
+from functools import partial
+from multiprocessing import Pool
+from tqdm import tqdm
+
+from utils.openai_api_utils import create_response_chat, create_response
+
+
+def get_answer_from_chat_model(prompt, logger=None, eng='gpt-3.5-turbo', temperature=0.0, timeout=20, max_try=0):
+    if eng in ["gpt-3.5-turbo", "gpt-3.5-turbo-16k", "gpt-3.5-turbo-0613", "gpt-3.5-turbo-16k-0613",
+               "gpt-4", "gpt-4-0613", "gpt-4-32k", "gpt-4-32k-0613", "gpt-3.5-turbo-1106"
+               ]:
+        is_success = False
+        num_exception = 0
+        [q, prompt] = prompt.split("======")
+        while not is_success:
+            if max_try > 0 and num_exception > max_try:
+                return ""
+            try:
+                response = create_response_chat([
+                            {"role": "system", "content": "Follow the given examples and answer the question."},
+                            {"role": "user", "content": prompt},
+                        ], eng, temperature, timeout)
+                return response['choices'][0]['message']["content"].strip()
+            except Exception as e:
+                is_print_exc = num_exception % 10 == 0
+                num_exception += 1
+                sleep_time = min(num_exception, 2)
+                logger.error(f"exception, repeat question: {q}", exc_info=is_print_exc)
+                logger.info(f"exception counter: {num_exception}, sleep {sleep_time} s")
+                time.sleep(sleep_time)
+                is_success = False
+    else:
+        raise ValueError("unknown api")
+
+
+def wrapper(idx_args, func):
+    idx, args = idx_args
+    res = func(args)
+    return idx, res
+
+
+def batch_get_chat_api(examples, eng, pre_fun, post_fun,
+                       logger=None, n_processes=8, temperature=0.7, timeout=20, max_try=0, **kwargs):
+    get_answer_func = partial(get_answer_from_chat_model, logger=logger, eng=eng, temperature=temperature, timeout=timeout, max_try=max_try)
+    get_answer_func = partial(get_answer_func, **kwargs)
+
+    prompts = [f"{_['question']}======{pre_fun(_)}" for _ in examples]
+
+    idx2res = {}
+    with Pool(n_processes) as p:
+        for idx, response in tqdm(p.imap_unordered(partial(wrapper, func=get_answer_func), enumerate(prompts)), total=len(prompts)):
+            idx2res[idx] = response
+
+    for idx, e in enumerate(examples):
+        post_fun(e, idx2res[idx])
+
+
+def batch_get_api(examples, eng, pre_fun, post_fun,
+                  logger=None, max_tokens=1024, temperature=0.0, timeout=20, max_try=0, **kwargs):
+    prompts = [pre_fun(_) for _ in examples]
+    is_success = False
+    num_exception = 0
+    while not is_success:
+        if max_try > 0 and num_exception > max_try:
+            return ""
+        try:
+            response = create_response(prompts, eng, max_tokens, temperature, timeout=timeout)
+            is_success = True
+        except Exception as e:
+            is_print_exc = num_exception % 10 == 0
+            num_exception += 1
+            sleep_time = num_exception
+            logger.error(f"exception, repeat question {examples[0]['question']}", exc_info=is_print_exc)
+            logger.info(f"exception counter: {num_exception}, sleep {sleep_time} s")
+            time.sleep(sleep_time)
+            is_success = False
+
+    for i, e in enumerate(examples):
+        reply = response['choices'][i]["text"]
+        post_fun(e, reply)
+
+
+def batch_get_api_merge(examples, eng, pre_fun, post_fun, logger=None, n_processes=8, temperature=0.7, timeout=20, max_try=0, **kwargs):
+    if eng in ("text-davinci-002", "text-davinci-003"):
+        batch_get_api(examples, eng, pre_fun=pre_fun, post_fun=post_fun,
+                      logger=logger, temperature=temperature, timeout=timeout, max_try=max_try, **kwargs)
+    else:
+        batch_get_chat_api(examples, eng, pre_fun, post_fun,
+                           logger=logger, n_processes=n_processes,
+                           temperature=temperature, timeout=timeout, max_try=max_try, **kwargs)
\ No newline at end of file

code_for_generating_data/code/utils/path_utils.py

+
+import os
+import torch
+
+
+class PathUtils(object):
+
+    def __init__(self):
+        pass
+
+    HOME_PATH = ""
+    DATA_HOME_PATH = os.path.join(HOME_PATH, "data")
+    Log_HOME_PATH = os.path.join(HOME_PATH, "log")
+    CONFIG_HOME_PATH = os.path.join(HOME_PATH, "configs")
+    FIGS_HOME_PATH = os.path.join(HOME_PATH, "figs")
+
+    @staticmethod
+    def set_path():
+        PathUtils.DATA_HOME_PATH = os.path.join(PathUtils.HOME_PATH, "data")
+        PathUtils.Log_HOME_PATH = os.path.join(PathUtils.HOME_PATH, "log")
+        PathUtils.CONFIG_HOME_PATH = os.path.join(PathUtils.HOME_PATH, "configs")
+        PathUtils.FIGS_HOME_PATH = os.path.join(PathUtils.HOME_PATH, "figs")
+
+    @staticmethod
+    def exists(file_name):
+        return os.path.exists(file_name)
+
+    @staticmethod
+    def create_dir(file_full_path):
+        os.makedirs(os.path.dirname(file_full_path), exist_ok=True)
+
+    @staticmethod
+    def get_job_home_path(dir_name):
+        _path = '{}/{}/'.format(PathUtils.Log_HOME_PATH, dir_name)
+        PathUtils.create_dir(_path)
+        return _path
+
+    @staticmethod
+    def get_log_home_path():
+        return PathUtils.Log_HOME_PATH
+
+    @staticmethod
+    def save_ckp(ckp, dir_name, identifier, index_key):
+        _path = "{}/{}/ckp-{}-{}".format(PathUtils.Log_HOME_PATH, dir_name, identifier, index_key)
+        torch.save(ckp, _path)
+
+    @staticmethod
+    def get_file_path(task_name, file_name):
+        return "{}/{}/{}".format(PathUtils.Log_HOME_PATH, task_name, file_name)
+
+    @staticmethod
+    def get_a_local_file_from_logpath(dir_name, identifier, index_key, file_name):
+        return "{}/{}/{}-{}-{}".format(PathUtils.Log_HOME_PATH, dir_name, identifier, index_key, file_name)
+
+    @staticmethod
+    def save_ckp_to_path(ckp, _path):
+        torch.save(ckp, _path)
+
+    @staticmethod
+    def load_ckp(dir_name, identifier, index_key):
+        _path = "{}/{}/ckp-{}-{}".format(PathUtils.Log_HOME_PATH, dir_name, identifier, index_key)
+        return torch.load(_path, map_location=torch.device('cpu'))
+
+    @staticmethod
+    def load_ckp_from_path(_path):
+        return torch.load(_path, map_location=torch.device('cpu'))
+
+
+
+

code_for_generating_data/code/utils/time_utils.py

+
+from datetime import datetime
+import time
+
+
+def sleep_minute(n_minute):
+    time.sleep(60 * n_minute)
+
+
+def sleep_sec(n_sec):
+    time.sleep(n_sec)
+
+
+class TimeUtils:
+    def __init__(self):
+        pass
+
+    DDYYYYMM = "%d%m%Y"
+    YYYY_MM_DD = "%Y-%m-%d"
+    YYYYMMDD = "%Y%m%d"
+    YYYYMMDDHHMMSS = "%Y-%m-%d %H:%M:%S"
+    YYYYMMDDHHMMSS_COMPACT = "%Y%m%d_%H%M%S"
+    YYYYMMDDHHMM_COMPACT = "%Y%m%d_%H%M"
+
+    @staticmethod
+    def get_now_str(fmt=YYYYMMDDHHMMSS_COMPACT):
+        return datetime.today().strftime(fmt)
+
+
+class TimeAccumulator(object):
+    def __init__(self):
+        self.total_time = 0  # ms
+
+    def add(self, tc):
+        self.total_time += tc
+
+    def get_total_time(self):
+        # return sec
+        return int(self.total_time / 1000)
+
+
+class TimeCounter(object):
+    def __init__(self):
+        self.start = time.time()
+        self.total_eval_time = 0  # sec
+
+    def restart(self):
+        self.start = time.time()
+
+    def add_eval_time(self, eval_time):
+        self.total_eval_time = self.total_eval_time + eval_time
+
+    def count(self):
+        return int(time.time() - self.start) - self.total_eval_time
+
+    def count_ms(self):
+        ts = time.time() - self.start
+        return int(ts * 1000 - self.total_eval_time*1000)
+

code_for_generating_data/configs/ansaug_cot_gsm8k.txt

+Question: Angelo and Melanie want to plan how many hours over the next week they should study together for their test next week. They have 2 chapters of their textbook to study and 4 worksheets to memorize. They figure out that they should dedicate 3 hours to each chapter of their textbook and 1.5 hours for each worksheet. If they plan to study no more than 4 hours each day, how many days should they plan to study total over the next week if they take a 10-minute break every hour, include 3 10-minute snack breaks each day, and 30 minutes for lunch each day?
+A: Let's think step by step.
+Angelo and Melanie think they should dedicate 3 hours to each of the 2 chapters, 3 hours x 2 chapters = 6 hours total.
+For the worksheets they plan to dedicate 1.5 hours for each worksheet, 1.5 hours x 4 worksheets = 6 hours total.
+Angelo and Melanie need to start with planning 12 hours to study, at 4 hours a day, 12 / 4 = 3 days.
+However, they need to include time for breaks and lunch. Every hour they want to include a 10-minute break, so 12 total hours x 10 minutes = 120 extra minutes for breaks.
+They also want to include 3 10-minute snack breaks, 3 x 10 minutes = 30 minutes.
+And they want to include 30 minutes for lunch each day, so 120 minutes for breaks + 30 minutes for snack breaks + 30 minutes for lunch = 180 minutes, or 180 / 60 minutes per hour = 3 extra hours.
+So Angelo and Melanie want to plan 12 hours to study + 3 hours of breaks = 15 hours total.
+They want to study no more than 4 hours each day, 15 hours / 4 hours each day = 3.75
+They will need to plan to study 4 days to allow for all the time they need.
+The answer is 4
+
+Question: Mark's basketball team scores 25 2 pointers, 8 3 pointers and 10 free throws.  Their opponents score double the 2 pointers but half the 3 pointers and free throws.  What's the total number of points scored by both teams added together?
+A: Let's think step by step.
+Mark's team scores 25 2 pointers, meaning they scored 25*2= 50 points in 2 pointers.
+His team also scores 6 3 pointers, meaning they scored 8*3= 24 points in 3 pointers
+They scored 10 free throws, and free throws count as one point so they scored 10*1=10 points in free throws.
+All together his team scored 50+24+10= 84 points
+Mark's opponents scored double his team's number of 2 pointers, meaning they scored 50*2=100 points in 2 pointers.
+His opponents scored half his team's number of 3 pointers, meaning they scored 24/2= 12 points in 3 pointers.
+They also scored half Mark's team's points in free throws, meaning they scored 10/2=5 points in free throws.
+All together Mark's opponents scored 100+12+5=117 points
+The total score for the game is both team's scores added together, so it is 84+117=201 points
+The answer is 201
+
+Question: Bella has two times as many marbles as frisbees. She also has 20 more frisbees than deck cards. If she buys 2/5 times more of each item, what would be the total number of the items she will have if she currently has 60 marbles?
+A: Let's think step by step.
+When Bella buys 2/5 times more marbles, she'll have increased the number of marbles by 2/5*60 = 24
+The total number of marbles she'll have is 60+24 = 84
+If Bella currently has 60 marbles, and she has two times as many marbles as frisbees, she has 60/2 = 30 frisbees.
+If Bella buys 2/5 times more frisbees, she'll have 2/5*30 = 12 more frisbees.
+The total number of frisbees she'll have will increase to 30+12 = 42
+Bella also has 20 more frisbees than deck cards, meaning she has 30-20 = 10 deck cards
+If she buys 2/5 times more deck cards, she'll have 2/5*10 = 4 more deck cards.
+The total number of deck cards she'll have is 10+4 = 14
+Together, Bella will have a total of 14+42+84 = 140 items
+The answer is 140
+
+Question: A group of 4 fruit baskets contains 9 apples, 15 oranges, and 14 bananas in the first three baskets and 2 less of each fruit in the fourth basket. How many fruits are there?
+A: Let's think step by step.
+For the first three baskets, the number of apples and oranges in one basket is 9+15=24
+In total, together with bananas, the number of fruits in one basket is 24+14=38 for the first three baskets.
+Since there are three baskets each having 38 fruits, there are 3*38=114 fruits in the first three baskets.
+The number of apples in the fourth basket is 9-2=7
+There are also 15-2=13 oranges in the fourth basket
+The combined number of oranges and apples in the fourth basket is 13+7=20
+The fourth basket also contains 14-2=12 bananas.
+In total, the fourth basket has 20+12=32 fruits.
+The four baskets together have 32+114=146 fruits.
+The answer is 146
+
+Question: You can buy 4 apples or 1 watermelon for the same price. You bought 36 fruits evenly split between oranges, apples and watermelons, and the price of 1 orange is $0.50. How much does 1 apple cost if your total bill was $66?
+A: Let's think step by step.
+If 36 fruits were evenly split between 3 types of fruits, then I bought 36/3 = 12 units of each fruit
+If 1 orange costs $0.50 then 12 oranges will cost $0.50 * 12 = $6
+If my total bill was $66 and I spent $6 on oranges then I spent $66 - $6 = $60 on the other 2 fruit types.
+Assuming the price of watermelon is W, and knowing that you can buy 4 apples for the same price and that the price of one apple is A, then 1W=4A
+If we know we bought 12 watermelons and 12 apples for $60, then we know that $60 = 12W + 12A
+Knowing that 1W=4A, then we can convert the above to $60 = 12(4A) + 12A
+$60 = 48A + 12A
+$60 = 60A
+Then we know the price of one apple (A) is $60/60= $1
+The answer is 1
+
+Question: Susy goes to a large school with 800 students, while Sarah goes to a smaller school with only 300 students.  At the start of the school year, Susy had 100 social media followers.  She gained 40 new followers in the first week of the school year, half that in the second week, and half of that in the third week.  Sarah only had 50 social media followers at the start of the year, but she gained 90 new followers the first week, a third of that in the second week, and a third of that in the third week.  After three weeks, how many social media followers did the girl with the most total followers have?
+A: Let's think step by step.
+After one week, Susy has 100+40 = 140 followers.
+In the second week, Susy gains 40/2 = 20 new followers.
+In the third week, Susy gains 20/2 = 10 new followers.
+In total, Susy finishes the three weeks with 140+20+10 = 170 total followers.
+After one week, Sarah has 50+90 = 140 followers.
+After the second week, Sarah gains 90/3 = 30 followers.
+After the third week, Sarah gains 30/3 = 10 followers.
+So, Sarah finishes the three weeks with 140+30+10 = 180 total followers.
+Thus, Sarah is the girl with the most total followers with a total of 180.
+The answer is 180
+
+Question: Sam bought a dozen boxes, each with 30 highlighter pens inside, for $10 each box. He rearranged five of these boxes into packages of six highlighters each and sold them for $3 per package. He sold the rest of the highlighters separately at the rate of three pens for $2. How much profit did he make in total, in dollars?
+A: Let's think step by step.
+Sam bought 12 boxes x $10 = $120 worth of highlighters.
+He bought 12 * 30 = 360 highlighters in total.
+Sam then took 5 boxes × 6 highlighters/box = 30 highlighters.
+He sold these boxes for 5 * $3 = $15
+After selling these 5 boxes there were 360 - 30 = 330 highlighters remaining.
+These form 330 / 3 = 110 groups of three pens.
+He sold each of these groups for $2 each, so made 110 * 2 = $220 from them.
+In total, then, he earned $220 + $15 = $235.
+Since his original cost was $120, he earned $235 - $120 = $115 in profit.
+The answer is 115
+
+Question: In a certain school, 2/3 of the male students like to play basketball, but only 1/5 of the female students like to play basketball. What percent of the population of the school do not like to play basketball if the ratio of the male to female students is 3:2 and there are 1000 students?
+A: Let's think step by step.
+The students are divided into 3 + 2 = 5 parts where 3 parts are for males and 2 parts are for females.
+Each part represents 1000/5 = 200 students.
+So, there are 3 x 200 = 600 males.
+And there are 2 x 200 = 400 females.
+Hence, 600 x 2/3 = 400 males play basketball.
+And 400 x 1/5 = 80 females play basketball.
+A total of 400 + 80 = 480 students play basketball.
+Therefore, 1000 - 480 = 520 do not like to play basketball.
+The percentage of the school that do not like to play basketball is 520/1000 * 100 = 52
+The answer is 52
\ No newline at end of file

code_for_generating_data/configs/ansaug_cot_math.txt

+Question: Kevin Kangaroo begins hopping on a number line at 0. He wants to get to 1, but he can hop only $\frac{1}{3}$ of the distance. Each hop tires him out so that he continues to hop $\frac{1}{3}$ of the remaining distance. How far has he hopped after five hops? Express your answer as a common fraction.
+A: Let's think step by step.
+Kevin hops $1/3$ of the remaining distance with every hop.
+His first hop takes $1/3$ closer.
+For his second hop, he has $2/3$ left to travel, so he hops forward $(2/3)(1/3)$.
+For his third hop, he has $(2/3)^2$ left to travel, so he hops forward $(2/3)^2(1/3)$.
+In general, Kevin hops forward $(2/3)^{k-1}(1/3)$ on his $k$th hop.
+We want to find how far he has hopped after five hops.
+This is a finite geometric series with first term $1/3$, common ratio $2/3$, and five terms.
+Thus, Kevin has hopped $\frac{\frac{1}{3}\left(1-\left(\frac{2}{3}\right)^5\right)}{1-\frac{2}{3}} = \boxed{\frac{211}{243}}$.
+The answer is \frac{211}{243}}
+
+Question: What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+3$?
+A: Let's think step by step.
+We rewrite the equation as $x^2 + 14x + y^2 - 4y = 10$ and then complete the square,
+resulting in  $(x+7)^2-49 + (y-2)^2-4=10$,
+or $(x+7)^2+(y-2)^2=63$.
+This is the equation of a circle with center $(-7, 2)$ and radius $\sqrt{63},$
+so the area of this region is $\pi r^2 = \boxed{63\pi}$.
+The answer is 63\pi
+
+Question: If $x^2+y^2=1$, what is the largest possible value of $|x|+|y|$?
+A: Let's think step by step.
+If $(x,y)$ lies on the circle,
+so does $(x,-y),$ $(-x,-y),$ and $(-x,-y),$ (which all give the same value of $|x| + |y|$),
+so we can assume that $x \ge 0$ and $y \ge 0.$
+Then $|x| + |y| = x + y.$  Squaring, we get
+\[(x + y)^2 = x^2 + 2xy + y^2 = 1 + 2xy.\]
+Note that $(x - y)^2 \ge 0.$
+Expanding, we get $x^2 - 2xy + y^2 \ge 0,$ so $2xy \le x^2 + y^2 = 1.$
+Hence,\[1 + 2xy \le 2,\]which means $x + y \le \sqrt{2}.$
+Equality occurs when $x = y = \frac{1}{\sqrt{2}},$
+so the maximum value of $|x| + |y|$ is $\boxed{\sqrt{2}}.$
+The answer is \sqrt{2}
+
+Question: If $f(x)=\frac{ax+b}{cx+d}, abcd\not=0$ and $f(f(x))=x$ for all $x$ in the domain of $f$, what is the value of $a+d$?
+A: Let's think step by step.
+The condition $f(f(x))$ means that $f$ is the inverse of itself,
+so its graph is symmetrical about the line $y = x$.
+With a rational function of this form, we will have two asymptotes:
+a vertical one at $x=-d/c$ if $cx+d$ does not divide $ax+b$,
+and a horizontal one at $y=a/c$,
+if we take the limit of $f(x)$ as $x$ goes to $\pm\infty$.
+In order for $f$ to be its own inverse, the intersection of the asymptotes must lie on the line $y=x$
+so that it and its asymptotes reflect onto themselves.
+This means that $-d/c=a/c$,
+and therefore $-d=a$ and $a+d=\boxed{0}$.
+The answer is 0
+
+Question: A math teacher requires Noelle to do one homework assignment for each of the first five homework points she wants to earn; for each of the next five homework points, she needs to do two homework assignments; and so on, so that to earn the $n^{\text{th}}$ homework point, she has to do $n\div5$ (rounded up) homework assignments. For example, when she has 11 points, it will take $12\div5=2.4\rightarrow3$ homework assignments to earn her $12^{\text{th}}$ point. What is the smallest number of homework assignments necessary to earn a total of 25 homework points?
+A: Let's think step by step.
+Noelle only has to do 1 homework assignment to earn her first point,
+and the same is true for each of her first five points.
+She must then do 2 homework assignments to earn her sixth point, seventh point, and so on, up to her tenth point.
+Continuing, we see that Noelle must do a total of \[1+1+1+1+1+2+2+2+2+2+\dots+5+5+5+5+5\] homework assignments to earn 25 points.
+This sum may be rewritten as $5(1+2+3+4+5)=5(15)=\boxed{75}$.
+The answer is 75
+
+Question: The quadratic equation $x^2+mx+n=0$ has roots that are twice those of $x^2+px+m=0,$ and none of $m,$ $n,$ and $p$ is zero. What is the value of $n/p?$
+A: Let's think step by step.
+Let $r_1$ and $r_2$ be the roots of $x^2+px+m=0.$
+Since the roots of $x^2+mx+n=0$ are $2r_1$ and $2r_2,$ we have the following relationships: \[
+m=r_1 r_2,\quad n=4r_1 r_2,\quad p=-(r_1+r_2), \quad\text{and}\quad
+m=-2(r_1+r_2).
+\] So \[
+n = 4m, \quad p = \frac{1}{2}m,
+\quad\text{and}\quad
+\frac{n}{p}=\frac{4m}{\frac{1}{2}m}=\boxed{8}.
+\]
+Alternatively, the roots of \[
+\left(\frac{x}{2}\right)^2 + p\left(\frac{x}{2}\right) + m = 0
+\] are twice those of $x^2 + px + m = 0.$
+Since the first equation is equivalent to $x^2 + 2px + 4m = 0,$
+we have \[m = 2p \quad\text{and}\quad n = 4m, \quad\text{so}\quad \frac{n}{p} = \boxed{8}.\]
+The answer is 8
+
+Question: Expand $(2z^2 + 5z - 6)(3z^3 - 2z + 1)$.
+A: Let's think step by step.
+$$\begin{array}{crrrrrrr}
+& & & 3z^3 & & -2z & + 1 & \\
+\times & & & & 2z^2 & +5z & -6 \\
+\cline{1-7}\rule{0pt}{0.17in}
+& & & -18z^3 & & +12z & -6 & \\
+& & +15z^4 & & -10z^2 & +5z & & \\
++ & 6z^5 & & -4z^3 & +2z^2 & & & \\
+\cline{1-7}\rule{0pt}{0.17in}
+& 6z^5 & +15z^4 & -22z^3 & - 8z^2 &+17z & -6 &
+\end{array}$$
+The answer is 6z^5+15z^4-22z^3-8z^2+17z-6}
+
+Question: Find the mean of all solutions for $x$ when $x^3 + 3x^2 - 10x = 0$.
+A: Let's think step by step.
+First, we factor the equation as $x(x^2 +3x - 10) = 0$.
+So, one solution is $x=0$ and the other two solutions are the solutions to $x^2 + 3x-10=0$.
+We could either factor the quadratic, or note that the sum of the solutions to this quadratic is $-(3/1)=-3$,
+so the mean of the three solutions to the original equation is $-3/3=\boxed{-1}$.
+The answer is -1
\ No newline at end of file

code_for_generating_data/configs/fobar_cot_gsm8k.txt

+You are an AI assistant to help me solve math problem.
+I first give you an original question with an unknown variable x, then I give you the answer to this original question.
+You help me determine the value of x.
+Follow the given examples and answer the question.
+
+Question: Randy has 60 mango trees on his farm. He also has x less than half as many coconut trees as mango trees. How many trees does Randy have in all on his farm?
+If we know the answer to the above question is 85, what is the value of unknown variable x?
+A: Let's think step by step.
+We know that Randy has 60 mango trees on his farm.
+We also know that he has x less than half as many coconut trees as mango trees. Let's use C to represent the number of coconut trees.
+So we can write: C = (1/2)*60 - x = 30 - x
+The total number of trees on Randy's farm is the sum of the number of mango trees and coconut trees: 60 + (30 - x) = 90 - x.
+We are given that the total number of trees on Randy's farm is 85, so we can write: 90 - x = 85
+Solving for x, we get: x = 5.
+The value of x is 5.
+
+Question: Joy can read 8 pages of a book in 20 minutes. How many hours will it take her to read x pages?
+If we know the answer to the above question is 5, what is the value of unknown variable x?
+A: Let's think step by step.
+We know that Joy can read 8 pages of a book in 20 minutes, or 8/20 pages per minute.
+To find out how many minutes it will take her to read x pages, we can use the formula:
+time = (number of pages) / (pages per minute)
+Substituting 8/20 for "pages per minute", we get:
+time = x / (8/20) = (20/8) * x = 2.5x
+We are given that the time it takes Joy to read x pages is 5 hours, or 300 minutes, so we can write: 2.5x = 300
+Solving for x, we get: x = 120.
+The value of x is 120.
+
+Question: In a truck, there are 26 pink hard hats, 15 green hard hats, and 24 yellow hard hats. If Carl takes away 4 pink hard hats, and John takes away x pink hard hats and twice as many green hard hats as the number of pink hard hats that he removed, then calculate the total number of hard hats that remained in the truck.
+If we know the answer to the above question is 43, what is the value of unknown variable x?
+A: Let's think step by step.
+We start with a total of 26 + 15 + 24 = 65 hard hats in the truck.
+Carl takes away 4 pink hard hats, leaving 26 - 4 = 22 pink hard hats.
+John takes away x pink hard hats and twice as many green hard hats as the number of pink hard hats he removed, which means he takes away 2x green hard hats.
+After John takes away the hard hats, the number of pink hard hats remaining is 22 - x, the number of green hard hats remaining is 15 - 2x, and the number of yellow hard hats remaining is still 24.
+The total number of hard hats remaining in the truck is the sum of the remaining pink, green, and yellow hard hats: (22 - x) + (15 - 2x) + 24 = 61 - 3x.
+We are given that the total number of hard hats remaining in the truck is 43, so we can write: 61 - 3x = 43.
+Solving for x, we get: x = 6.
+The value of x is 6.
+
+Question: Each bird eats 12 beetles per day, each snake eats 3 birds per day, and each jaguar eats 5 snakes per day. If there are x jaguars in a forest, how many beetles are eaten each day?
+If we know the answer to the above question is 1080, what is the value of unknown variable x?
+A: Let's think step by step.
+We know that each bird eats 12 beetles per day.
+We also know that each snake eats 3 birds per day, which means each snake eats 3 * 12 = 36 beetles per day.
+Similarly, each jaguar eats 5 snakes per day, which means each jaguar eats 5 * 36 = 180 beetles per day.
+If there are x jaguars in the forest, then the total number of beetles eaten per day is x * 180.
+We are given that the total number of beetles eaten per day is 1080, so we can write: x * 180 = 1080.
+Dividing both sides by 180, we get: x = 6.
+The value of x is 6.
+
+Question: Mr. Sam shared a certain amount of money between his two sons, Ken and Tony. If Ken got x, and Tony got twice as much as Ken, how much was the money shared?
+If we know the answer to the above question is 5250, what is the value of unknown variable x?
+A: Let's think step by step.
+We know that Tony got twice as much as Ken, which means Tony got 2x.
+The total amount of money shared is the sum of what Ken and Tony got: x + 2x = 3x.
+We are given that the total amount of money shared is 5250, so we can write: 3x = 5250.
+Dividing both sides by 3, we get: x = 1750.
+The value of x is 1750.
+
+Question: It's Ava's birthday party. Her parents bought a unicorn piñata for $13 and filled it with all of her favorite treats. They bought 4 bags of Reese's for $9 per bag, 3 bags of Snickers for $5 per bag, and 5 bags of Skittles for x per bag. How much did the unicorn piñata and the treats cost altogether?
+If we know the answer to the above question is 99, what is the value of unknown variable x?
+A: Let's think step by step.
+The unicorn piñata cost $13.
+The cost of the Reese's is 4 * $9 = $36.
+The cost of the Snickers is 3 * $5 = $15.
+Let's find the cost of the Skittles. We know that there are 5 bags of Skittles, and each bag costs x. So the total cost of the Skittles is 5x.
+The total cost of everything is the sum of the cost of the piñata and the cost of the treats: $13 + $36 + $15 + 5x.
+We are given that the total cost is $99, so we can write: $13 + $36 + $15 + 5x = $99.
+Simplifying the left side, we get: $64 + 5x = $99.
+Subtracting $64 from both sides, we get: 5x = $35.
+Dividing both sides by 5, we get: x = $7.
+The value of x is $7.
+
+Question: Liza bought x kilograms of butter to make cookies. She used one-half of it for chocolate chip cookies, one-fifth of it for peanut butter cookies, and one-third of the remaining butter for sugar cookies. How many kilograms of butter are left after making those three kinds of cookies?
+If we know the answer to the above question is 2, what is the value of unknown variable x?
+A: Let's think step by step.
+Liza bought x kilograms of butter.
+She used one-half of it for chocolate chip cookies, which means she used (1/2)*x kilograms of butter for chocolate chip cookies.
+She used one-fifth of it for peanut butter cookies, which means she used (1/5)*x kilograms of butter for peanut butter cookies.
+The total amount of butter used for these two kinds of cookies is: (1/2)*x + (1/5)*x = (5/10)*x + (2/10)*x = (7/10)*x.
+The remaining amount of butter is: x - (7/10)*x = (3/10)x.
+She used one-third of the remaining butter for sugar cookies, which means she used (1/3)(3/10)*x = (1/10)*x kilograms of butter for sugar cookies.
+The amount of butter left after making all three kinds of cookies is: (3/10)*x - (1/10)*x = (2/10)*x = 0.2x.
+We are given that the amount of butter left is 2 kilograms, so we can write: 0.2x = 2.
+Solving for x, we get: x = 10.
+The value of x is 10.
+
+Question: Carly collected x starfish with 5 arms each and one seastar with 14 arms. How many arms do the animals she collected have in total?
+If we know the answer to the above question is 49, what is the value of unknown variable x?
+A: Let's think step by step.
+Carly collected x starfish with 5 arms each, which means the starfish have a total of 5x arms.
+She also collected one seastar with 14 arms.
+The total number of arms is the sum of the number of arms of the starfish and the seastar: 5x + 14.
+We are given that the total number of arms is 49, so we can write: 5x + 14 = 49.
+Subtracting 14 from both sides, we get: 5x = 35.
+Dividing both sides by 5, we get: x = 7.
+The value of x is 7.
\ No newline at end of file

code_for_generating_data/configs/fobar_cot_math.txt

+You are an AI assistant to help me solve math problem.
+I first give you an original question with an unknown variable $X$, then I give you the answer to this original question.
+You help me determine the value of $X$.
+Follow the given examples and answer the question.
+
+Question: On a map, a 12-centimeter length represents $X$ kilometers.  How many kilometers does a 17-centimeter length represent?
+### If we know the answer to the above question is 102, what is the value of unknown variable $X$?
+A: Let's think step by step.
+We know that on the map, a 12-centimeter length represents $X$ kilometers.
+To find out how many kilometers a 17-centimeter length represents, we can set up a proportion using the given information:
+12 centimeters / $X$ kilometers = 17 centimeters / 102 kilometers
+We can cross-multiply and solve for $X$:
+12 * 102 = 17 * $X$
+1224 = 17 * $X$
+Dividing both sides by 17, we get:
+$X$ = 72
+The value of X is 72.
+
+Question: If the sum of the squares of nonnegative real numbers $a,b,$ and $c$ is $39$, and $ab + bc + ca = X$, then what is the sum of $a,b,$ and $c$?
+### If we know the answer to the above question is 9, what is the value of unknown variable $X$?
+A: Let's think step by step.
+We are given that the sum of the squares of nonnegative real numbers $a$, $b$, and $c$ is $39$, and $ab + bc + ca = X$.
+To find the sum of $a$, $b$, and $c$, we need to determine the value of $X$.
+We can start by using the given information to set up an equation.
+We know that $(a^2 + b^2 + c^2) = 39$ and $ab + bc + ca = X$.
+We can rewrite the equation $(a^2 + b^2 + c^2)$ as $(a^2 + b^2 + c^2 + 2ab + 2bc + 2ca - 2ab - 2bc - 2ca)$.
+Using this, we can expand the equation as follows:
+$(a^2 + b^2 + c^2 + 2ab + 2bc + 2ca - 2ab - 2bc - 2ca) = 39$
+Simplifying this equation gives us:
+$(a + b + c)^2 = 39 + 2(ab + bc + ca)$
+$(a + b + c)^2 = 39 + 2X$
+Now, we know that the sum of $a$, $b$, and $c$ is the square root of $(a + b + c)^2$. Let's call this sum $S$.
+$S = \sqrt{(a + b + c)^2}$
+$S = \sqrt{39 + 2X}$
+Given that the sum of $a$, $b$, and $c$ is 9, we can set up the equation:
+$9 = \sqrt{39 + 2X}$
+To solve for $X$, we can square both sides of the equation:
+$81 = 39 + 2X$
+Subtracting 39 from both sides, we get:
+$42 = 2X$
+Dividing both sides by 2, we find:
+$X = 21$
+The value of X is 21.
+
+Question: The mean of $5,8$ and $17$ is equal to the mean of $X$ and $y$. What is the value of $y$?
+### If we know the answer to the above question is 8, what is the value of unknown variable $X$?
+A: Let's think step by step.
+We are given that the mean of 5, 8, and 17 is equal to the mean of $X$ and $y$.
+To find the value of $y$, we need to determine the value of $X$.
+The mean of a set of numbers is found by summing all the numbers and dividing by the total count.
+For the given set of numbers, the mean is:
+(5 + 8 + 17) / 3 = 30 / 3 = 10
+Since the mean of $X$ and $y$ is also 10, we can set up the equation:
+(X + y) / 2 = 10
+Multiplying both sides by 2, we get:
+X + y = 20
+Given that the value of $y$ is 8, we can substitute it into the equation:
+X + 8 = 20
+Subtracting 8 from both sides, we find:
+X = 12
+The value of X is 12.
+
+Question: A taxi ride costs \\$1.50$ plus $\\$0.25$ per mile traveled.  How much, in dollars, does a $X$ mile taxi ride cost?
+### If we know the answer to the above question is 2.75, what is the value of unknown variable $X$?
+A: Let's think step by step.
+We are given that a taxi ride costs $1.50 plus $0.25 per mile traveled.
+To find the cost of a $X$ mile taxi ride, we can set up an equation using the given information.
+The equation can be written as:
+Cost = $1.50 + $0.25 * X
+We are given that the cost is $2.75, so we can substitute this value into the equation:
+$2.75 = $1.50 + $0.25 * X
+Now we can solve for $X$.
+Subtracting $1.50 from both sides of the equation, we get:
+$2.75 - $1.50 = $0.25 * X
+$1.25 = $0.25 * X
+Dividing both sides of the equation by $0.25, we find:
+X = 5
+The value of X is 5.
+
+Question: How many ways are there to put 5 balls in $X$ boxes if the balls are not distinguishable but the boxes are?
+### If we know the answer to the above question is 6, what is the value of unknown variable $X$?
+A: Let's think step by step.
+We want to find the value of $X$ in the given situation.
+We are told that the balls are not distinguishable, but the boxes are.
+This means that the arrangement of balls in the boxes does not matter, and we only need to consider the number of balls in each box.
+To solve this, let's use the concept of stars and bars.
+We can imagine the balls as stars and the boxes as bars.
+The number of ways to distribute the balls among the boxes is equal to the number of ways to arrange the stars and bars.
+In this case, we have 5 balls and $X$ boxes.
+So, we need to distribute the 5 balls among $X$ boxes using stars and bars.
+The number of ways to arrange the stars and bars can be calculated using the formula:
+Number of ways = (Number of objects + Number of gaps) choose (Number of gaps)
+In this case, the number of objects is 5 (balls) and the number of gaps is $X-1$ (the spaces between the bars).
+We are given that the number of ways is 6, so we can write:
+6 = (5 + $X-1$) choose ($X-1$)
+Simplifying, we have:
+6 = (4 + $X$) choose ($X-1$)
+To find the value of $X$, we can try different values and solve for $X$.
+Let's start with $X = 2$:
+6 = (4 + 2) choose (2-1)
+6 = 6 choose 1
+6 = 6
+The equation holds true for $X = 2$.
+The value of X is 2.
+
+Question: If $x - y = X$ and $x + y = 6$, what is the value of $y$?
+### If we know the answer to the above question is -3, what is the value of unknown variable $X$?
+A: Let's think step by step.
+We are given the equations:
+$x - y = X$
+$x + y = 6$
+To find the value of $y$, we can solve these equations simultaneously.
+We can add the two equations together to eliminate $x$:
+$(x - y) + (x + y) = X + 6$
+$2x = X + 6$
+Now, we can solve for $x$ by dividing both sides of the equation by 2:
+$x = \frac{X + 6}{2}$
+Substituting this value of $x$ into the second equation, we have:
+$\frac{X + 6}{2} + y = 6$
+Multiplying both sides of the equation by 2 to eliminate the fraction, we get:
+$X + 6 + 2y = 12$
+Simplifying, we have:
+$2y = 12 - X - 6$
+$2y = 6 - X$
+Dividing both sides of the equation by 2, we find:
+$y = \frac{6 - X}{2}$
+Given that the value of $y$ is -3, we can substitute it into the equation:
+$-3 = \frac{6 - X}{2}$
+Multiplying both sides of the equation by 2 to eliminate the fraction, we get:
+$-6 = 6 - X$
+Subtracting 6 from both sides of the equation, we find:
+$-12 = -X$
+Dividing both sides of the equation by -1, we get:
+$X = 12$
+The value of X is 12.
+
+Question: What is the sum of the first $X$ odd positive integers?
+### If we know the answer to the above question is 100, what is the value of unknown variable $X$?
+A: Let's think step by step.
+We want to find the value of $X$ in the given situation.
+The sum of the first $X$ odd positive integers can be found using the formula:
+Sum = $X^2$
+We are given that the sum is 100, so we can write:
+$X^2 = 100$
+To find the value of $X$, we can take the square root of both sides of the equation:
+$X = \sqrt{100}$
+Taking the square root of 100 gives us two possible values, +10 and -10. However, since we are looking for the number of odd positive integers, $X$ must be a positive value.
+Therefore, the value of $X$ is 10.
+
+Question: The sum of two numbers is $X$. Their difference is $4$. What is the larger of the two numbers?
+### If we know the answer to the above question is 17, what is the value of unknown variable $X$?
+A: Let's think step by step.
+Let's call the larger number $a$ and the smaller number $b$.
+According to the given information, we can set up two equations:
+$a + b = X$ (Equation 1)
+$a - b = 4$ (Equation 2)
+To find the larger number, which is $a$, we can solve this system of equations.
+We can add Equation 1 and Equation 2 together to eliminate $b$:
+$(a + b) + (a - b) = X + 4$
+$2a = X + 4$
+Now, we can solve for $a$ by dividing both sides of the equation by 2:
+$a = \frac{X + 4}{2}$
+Given that the value of the larger number $a$ is 17, we can substitute it into the equation:
+$17 = \frac{X + 4}{2}$
+Multiplying both sides of the equation by 2 to eliminate the fraction, we get:
+$34 = X + 4$
+Subtracting 4 from both sides of the equation, we find:
+$30 = X$
+The value of X is 30.
\ No newline at end of file

code_for_generating_data/configs/rephrase_cot_gsm8k.txt

+You are an AI assistant to help me rephrase questions.
+Follow the given examples.
+
+Question: Angelo and Melanie want to plan how many hours over the next week they should study together for their test next week. They have 2 chapters of their textbook to study and 4 worksheets to memorize. They figure out that they should dedicate 3 hours to each chapter of their textbook and 1.5 hours for each worksheet. If they plan to study no more than 4 hours each day, how many days should they plan to study total over the next week if they take a 10-minute break every hour, include 3 10-minute snack breaks each day, and 30 minutes for lunch each day?
+Rephrase the above question: Angelo and Melanie need to study 2 chapters in their textbook and 4 worksheets for their upcoming test. They have planned to dedicate 3 hours for each chapter and 1.5 hours for each worksheet. They can study for a maximum of 4 hours each day, taking into account 10-minute breaks every hour, 3 10-minute snack breaks per day, and 30 minutes for lunch. How many days do they need to study in total over the next week to complete their study plan?
+
+Question: Leah had 32 chocolates and her sister had 42. If they ate 35, how many pieces do they have left in total?
+Rephrase the above question: If Leah had 32 chocolates and her sister had 42, and they both consumed 35 chocolates, what is the total number of chocolates that they have left?
+
+Question: Olivia has $23. She bought five bagels for $3 each. How much money does she have left?
+Rephrase the above question: What is the amount of money that Olivia has left after purchasing five bagels for $3 each, if she initially had $23?
+
+Question: There were nine computers in the server room. Five more computers were installed each day, from monday to thursday. How many computers are now in the server room?
+Rephrase the above question: If there were initially nine computers in the server room and five more computers were added each day from Monday to Thursday, what is the current total number of computers in the server room?
+
+Question: Michael had 58 golf balls. On tuesday, he lost 23 golf balls. On wednesday, he lost 2 more. How many golf balls did he have at the end of wednesday?
+Rephrase the above question: After losing 23 golf balls on Tuesday and an additional 2 on Wednesday, how many golf balls does Michael have left if he initially had 58 golf balls?
+
+Question: Jason had 20 lollipops. He gave Denny some lollipops. Now Jason has 12 lollipops. How many lollipops did Jason give to Denny?
+Rephrase the above question: If Jason initially had 20 lollipops and now has 12 after giving some to Denny, how many lollipops did he give to Denny?
+
+Question: Sam bought a dozen boxes, each with 30 highlighter pens inside, for $10 each box. He rearranged five of these boxes into packages of six highlighters each and sold them for $3 per package. He sold the rest of the highlighters separately at the rate of three pens for $2. How much profit did he make in total, in dollars?
+Rephrase the above question: Sam purchased 12 boxes, each containing 30 highlighter pens, at $10 per box. He repackaged five of these boxes into sets of six highlighters and sold them for $3 per set. He sold the remaining highlighters individually at a rate of three pens for $2. What is the total profit he made in dollars?
+
+Question: There are 15 trees in the grove. Grove workers will plant trees in the grove today. After they are done, there will be 21 trees. How many trees did the grove workers plant today?
+Rephrase the above question: If there were initially 15 trees in the grove and the grove workers are planning to plant more trees today, resulting in a total of 21 trees, how many trees did the workers plant today?
\ No newline at end of file

code_for_generating_data/configs/rephrase_cot_math.txt

+You are an AI assistant to help me rephrase questions.
+Follow the given examples.
+
+Question: Kevin Kangaroo begins hopping on a number line at 0. He wants to get to 1, but he can hop only $\frac{1}{3}$ of the distance. Each hop tires him out so that he continues to hop $\frac{1}{3}$ of the remaining distance. How far has he hopped after five hops? Express your answer as a common fraction.
+Rephrase the above question: Starting at 0 on a number line, Kevin Kangaroo aims to reach 1 by hopping only 1/3 of the distance each time. As he gets tired, he continues to hop 1/3 of the remaining distance. After completing five hops, what is the total distance he has covered, expressed as a common fraction?
+
+Question: What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+3$?
+Rephrase the above question: Determine the area of the region described by the equation $x^2+y^2 - 7 = 4y-14x+3$?
+
+Question: If $x^2+y^2=1$, what is the largest possible value of $|x|+|y|$?
+Rephrase the above question: What is the maximum value possible for |x| + |y| if x^2 + y^2 = 1?
+
+Question: If $f(x)=\frac{ax+b}{cx+d}, abcd\not=0$ and $f(f(x))=x$ for all $x$ in the domain of $f$, what is the value of $a+d$?
+Rephrase the above question: Given that $f(x) = \frac{ax + b}{cx + d}$, with all variables not equal to 0, and $f(f(x)) = x$ for all x within the domain of f, what is the value of $a + d$?
+
+Question: A math teacher requires Noelle to do one homework assignment for each of the first five homework points she wants to earn; for each of the next five homework points, she needs to do two homework assignments; and so on, so that to earn the $n^{\text{th}}$ homework point, she has to do $n\div5$ (rounded up) homework assignments. For example, when she has 11 points, it will take $12\div5=2.4\rightarrow3$ homework assignments to earn her $12^{\text{th}}$ point. What is the smallest number of homework assignments necessary to earn a total of 25 homework points?
+Rephrase the above question: Noelle's math teacher has a system where she needs to complete one homework assignment for each of the first five points, two assignments for each of the next five points, and so on, with the number of assignments required for the nth point being n divided by 5 (rounded up). For instance, to get her 12th point, she needs to complete 3 assignments (12/5 = 2.4, rounded up to 3). What is the minimum number of homework assignments Noelle must complete to earn a total of 25 points?
+
+Question: The quadratic equation $x^2+mx+n=0$ has roots that are twice those of $x^2+px+m=0,$ and none of $m,$ $n,$ and $p$ is zero. What is the value of $n/p?$
+Rephrase the above question: For the quadratic equation $x^2 + mx + n = 0$, the roots are twice the roots of $x^2 + px + m = 0$. None of the variables $m$, $n$, and $p$ are zero. What is the value of $n/p$?
+
+Question: Expand $(2z^2 + 5z - 6)(3z^3 - 2z + 1)$.
+Rephrase the above question: What is the expanded form of $(2z^2 + 5z - 6)(3z^3 - 2z + 1)$?
+
+Question: Find the mean of all solutions for $x$ when $x^3 + 3x^2 - 10x = 0$.
+Rephrase the above question: What is the average of all the solutions for $x$ in the equation $x^3 + 3x^2 - 10x = 0$?
\ No newline at end of file

code_for_generating_data/configs/sv_cot_gsm8k.txt

+You are an AI assistant to help me solve math problem.
+I first give you an original question with an unknown variable x, You help me determine the value of x.
+Follow the given examples and answer the question.
+
+Question: Randy has 60 mango trees on his farm. He also has x less than half as many coconut trees as mango trees. Randy has 85 trees in all on his farm. What is the value of unknown variable x?
+A: Let's think step by step.
+To solve this problem, we need to set up an equation based on the given information and then solve for the unknown variable x.
+Let's break down the information given:
+Randy has 60 mango trees.
+Randy has x less than half as many coconut trees as mango trees.
+Randy has 85 trees in total.
+We can set up the equation as follows:
+Number of mango trees + Number of coconut trees = Total number of trees
+60 + (60/2 - x) = 85
+Let's simplify and solve for x:
+60 + 30 - x = 85
+90 - x = 85
+To isolate x, we subtract 90 from both sides of the equation:
+90 - x - 90 = 85 - 90
+-x = -5
+Finally, we multiply both sides of the equation by -1 to solve for x:
+x = 5
+The value of x is 5.
+
+Question: Joy can read 8 pages of a book in 20 minutes. It will take her 5 hours to read x pages. What is the value of unknown variable x?
+A: Let's think step by step.
+To solve this problem, we need to determine the value of x, which represents the number of pages Joy will read in 5 hours.
+We know that Joy can read 8 pages in 20 minutes. Let's find out how many pages she can read in 1 minute:
+8 pages / 20 minutes = 0.4 pages per minute
+Now, let's calculate how many pages Joy can read in 5 hours:
+5 hours = 5 * 60 = 300 minutes
+0.4 pages per minute * 300 minutes = 120 pages
+Therefore, the value of the unknown variable x is 120. Joy will read 120 pages in 5 hours.
+The value of x is 120.
+
+Question: In a truck, there are 26 pink hard hats, 15 green hard hats, and 24 yellow hard hats. If Carl takes away 4 pink hard hats, and John takes away x pink hard hats and twice as many green hard hats as the number of pink hard hats that he removed, The total number of hard hats that remained in the truck is 43. What is the value of unknown variable x?
+A: Let's think step by step.
+To solve this problem, we need to set up an equation based on the given information and then solve for the unknown variable x.
+Let's break down the information given:
+Number of pink hard hats: 26 - 4 (Carl takes away 4 pink hard hats)
+Number of green hard hats: 15
+Number of yellow hard hats: 24
+Total number of hard hats: 43
+We can set up the equation as follows:
+Number of pink hard hats - (x + 2x) + Number of green hard hats + Number of yellow hard hats = Total number of hard hats
+26 - 4 - (x + 2x) + 15 + 24 = 43
+Let's simplify and solve for x:
+22 - 3x + 15 + 24 = 43
+61 - 3x = 43
+To isolate x, we subtract 61 from both sides of the equation:
+61 - 3x - 61 = 43 - 61
+-3x = -18
+Finally, we divide both sides of the equation by -3 to solve for x:
+x = -18 / -3
+x = 6
+The value of x is 6.
+
+Question: Each bird eats 12 beetles per day, each snake eats 3 birds per day, and each jaguar eats 5 snakes per day. If there are x jaguars in a forest, 1080 beetles are eaten each day. What is the value of unknown variable x?
+A: Let's think step by step.
+To solve this problem, we need to determine the value of x, which represents the number of jaguars in the forest.
+Let's break down the information given:
+Number of beetles eaten by each bird per day: 12
+Number of birds eaten by each snake per day: 3
+Number of snakes eaten by each jaguar per day: 5
+Total number of beetles eaten per day: 1080
+We can set up the equation as follows:
+Number of beetles eaten by each bird per day * Number of birds eaten by each snake per day * Number of snakes eaten by each jaguar per day * Number of jaguars = Total number of beetles eaten per day
+12 * 3 * 5 * x = 1080
+Let's simplify and solve for x:
+12 * 3 * 5 * x = 1080
+180x = 1080
+To isolate x, we divide both sides of the equation by 180:
+180x / 180 = 1080 / 180
+x = 6
+The value of x is 6.
+
+Question: Mr. Sam shared a certain amount of money between his two sons, Ken and Tony. If Ken got x, and Tony got twice as much as Ken, the money was shared 5250. What is the value of unknown variable x?
+A: Let's think step by step.
+To solve this problem, we need to determine the value of x, which represents the amount of money Ken received from Mr. Sam.
+We know that Tony received twice as much money as Ken. Therefore, Tony received 2x.
+The total amount of money shared between Ken and Tony is 5250.
+We can set up the equation as follows:
+Amount of money Ken received + Amount of money Tony received = Total amount of money shared
+x + 2x = 5250
+Let's simplify and solve for x:
+3x = 5250
+To isolate x, we divide both sides of the equation by 3:
+3x / 3 = 5250 / 3
+x = 1750
+The value of x is 1750.
+
+Question: It's Ava's birthday party. Her parents bought a unicorn piñata for $13 and filled it with all of her favorite treats. They bought 4 bags of Reese's for $9 per bag, 3 bags of Snickers for $5 per bag, and 5 bags of Skittles for x per bag. The unicorn piñata and the treats cost 99 altogether. What is the value of unknown variable x?
+A: Let's think step by step.
+To solve this problem, we need to determine the value of x, which represents the cost of each bag of Skittles.
+Let's break down the information given:
+Cost of the unicorn piñata: $13
+Number of bags of Reese's: 4
+Cost per bag of Reese's: $9
+Number of bags of Snickers: 3
+Cost per bag of Snickers: $5
+Number of bags of Skittles: 5
+Cost per bag of Skittles: x
+Total cost of the unicorn piñata and treats: $99
+We can set up the equation as follows:
+Cost of the unicorn piñata + (Number of bags of Reese's * Cost per bag of Reese's) + (Number of bags of Snickers * Cost per bag of Snickers) + (Number of bags of Skittles * Cost per bag of Skittles) = Total cost of the unicorn piñata and treats
+$13 + (4 * $9) + (3 * $5) + (5 * x) = $99
+Let's simplify and solve for x:
+$13 + $36 + $15 + 5x = $99
+$64 + 5x = $99
+To isolate x, we subtract $64 from both sides of the equation:
+$64 - $64 + 5x = $99 - $64
+5x = $35
+To solve for x, we divide both sides of the equation by 5:
+x = $35 / 5
+x = $7
+The value of x is $7.
+
+Question: Liza bought x kilograms of butter to make cookies. She used one-half of it for chocolate chip cookies, one-fifth of it for peanut butter cookies, and one-third of the remaining butter for sugar cookies. There are 2 kilograms of butter left after making those three kinds of cookies. What is the value of unknown variable x?
+A: Let's think step by step.
+To solve this problem, we need to determine the value of x, which represents the initial amount of butter Liza bought in kilograms.
+Let's break down the information given:
+Amount of butter used for chocolate chip cookies: 1/2x
+Amount of butter used for peanut butter cookies: 1/5x
+Amount of butter used for sugar cookies: 1/3 * (x - (1/2x + 1/5x))
+Amount of butter left: 2 kilograms
+We can set up the equation as follows:
+Amount of butter used for chocolate chip cookies + Amount of butter used for peanut butter cookies + Amount of butter used for sugar cookies + Amount of butter left = Initial amount of butter
+1/2x + 1/5x + 1/3 * (x - (1/2x + 1/5x)) + 2 = x
+Let's simplify and solve for x:
+(5/10)x + (2/10)x + (1/3)(x - (7/10)x) + 2 = x
+(7/10)x + (1/3)(3/10)x + 2 = x
+(7/10)x + (1/10)x + 2 = x
+(8/10)x + 2 = x
+To isolate x, we subtract (8/10)x from both sides of the equation:
+(8/10)x - (8/10)x + 2 = x - (8/10)x
+2 = (2/10)x
+To solve for x, we multiply both sides of the equation by 10/2:
+2 * (10/2) = (2/10)x * (10/2)
+10 = x
+The value of x is 10.
+
+Question: Carly collected x starfish with 5 arms each and one seastar with 14 arms. The animals she collected have 49 arms in total. What is the value of unknown variable x?
+A: Let's think step by step.
+To solve this problem, we need to determine the value of x, which represents the number of starfish with 5 arms that Carly collected.
+Let's break down the information given:
+Number of starfish with 5 arms: x
+Number of seastars with 14 arms: 1
+Total number of arms: 49
+We can set up the equation as follows:
+Number of starfish with 5 arms * Number of arms per starfish + Number of seastars with 14 arms * Number of arms per seastar = Total number of arms
+x * 5 + 1 * 14 = 49
+Let's simplify and solve for x:
+5x + 14 = 49
+To isolate x, we subtract 14 from both sides of the equation:
+5x + 14 - 14 = 49 - 14
+5x = 35
+To solve for x, we divide both sides of the equation by 5:
+x = 35 / 5
+x = 7
+The value of x is 7.
\ No newline at end of file

code_for_generating_data/configs/sv_cot_math.txt

+You are an AI assistant to help me solve math problem.
+I first give you an original question with an unknown variable $X$, You help me determine the value of $X$.
+Follow the given examples and answer the question.
+
+Question: On a map, a 12-centimeter length represents $X$ kilometers.  A 17-centimeter length represents 102 kilometers. What is the value of unknown variable $X$?
+A: Let's think step by step.
+To solve this problem, we need to determine the value of X, which represents the number of kilometers represented by a 12-centimeter length on the map.
+We know that a 17-centimeter length represents 102 kilometers. Let's find out the ratio of kilometers to centimeters:
+102 kilometers / 17 centimeters = 6 kilometers per centimeter
+Now, we can calculate the value of X:
+12 centimeters * 6 kilometers per centimeter = 72 kilometers
+Therefore, the value of the unknown variable X is 72 kilometers.
+The value of X is 72.
+
+Question: If the sum of the squares of nonnegative real numbers $a,b,$ and $c$ is $39$, and $ab + bc + ca = X$, the sum of $a$, $b$, and $c$ is 9. What is the value of unknown variable $X$?
+A: Let's think step by step.
+We know that the sum of the squares of the three nonnegative real numbers is 39:
+a^2 + b^2 + c^2 = 39
+We also know that the sum of the three numbers is 9:
+a + b + c = 9
+To find the value of X, which represents the value of ab + bc + ca, we can use the following identity:
+(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)
+Substituting the given values:
+9^2 = 39 + 2X
+81 = 39 + 2X
+2X = 81 - 39
+2X = 42
+X = 42 / 2
+X = 21
+The value of X is 21.
+
+Question: The mean of $5,8$ and $17$ is equal to the mean of $X$ and $y$. The value of $y$ is 8. What is the value of unknown variable $X$?
+A: Let's think step by step.
+We are given that the mean of 5, 8, and 17 is equal to the mean of X and y. We know that y is equal to 8. Let's denote the mean of X and 8 as M.
+The mean of 5, 8, and 17 is given by:
+(5 + 8 + 17) / 3 = 30 / 3 = 10
+We are told that this mean is equal to the mean of X and 8, so we can set up the equation:
+M = (X + 8) / 2
+Since M is equal to 10, we can substitute it into the equation:
+10 = (X + 8) / 2
+To solve for X, we can multiply both sides of the equation by 2:
+20 = X + 8
+Subtracting 8 from both sides gives us:
+X = 20 - 8
+X = 12
+The value of X is 12.
+
+Question: A taxi ride costs \\$1.50$ plus $\\$0.25$ per mile traveled.  How much, in dollars, a $X$ mile taxi ride costs 2.75. What is the value of unknown variable $X$?
+A: Let's think step by step.
+We are given that a taxi ride costs $1.50 plus $0.25 per mile traveled. Let's denote the cost of a taxi ride as C and the number of miles traveled as X.
+According to the given information, the cost C can be calculated using the formula:
+C = $1.50 + $0.25X
+We are also given that the cost of a taxi ride is $2.75. We can set up the equation:
+$2.75 = $1.50 + $0.25X
+To solve for X, we can subtract $1.50 from both sides of the equation:
+$2.75 - $1.50 = $0.25X
+Simplifying the left side gives us:
+$1.25 = $0.25X
+To isolate X, we can divide both sides of the equation by $0.25:
+$1.25 / $0.25 = X
+Simplifying the left side gives us:
+5 = X
+The value of X is 5.
+
+Question: There are 6 ways to put 5 balls in $X$ boxes if the balls are not distinguishable but the boxes are. What is the value of unknown variable $X$?
+A: Let's think step by step.
+We are given that there are 6 ways to put 5 balls in X boxes, where the balls are not distinguishable but the boxes are.
+To solve for X, we need to find the number of ways to distribute the balls among the boxes.
+This problem can be solved using a combinatorial approach, specifically using stars and bars.
+Since the balls are not distinguishable, we can think of them as stars. We need to distribute these stars among the X boxes, which can be represented by bars.
+To distribute 5 stars among X boxes, we need X-1 bars to separate the boxes.
+So, we have a total of 5 stars and X-1 bars, which gives us a total of 5 + (X-1) = X + 4 objects.
+We need to select the positions of the stars among the X + 4 objects, which can be done in (X + 4 choose 5) ways.
+Given that there are 6 ways to put the balls in the boxes, we can equate it to the calculated number of ways:
+(X + 4 choose 5) = 6
+To find the value of X, we can try different values until we find a combination that satisfies the equation.
+By testing different values, we find that X = 2 satisfies the equation:
+(2 + 4 choose 5) = 6
+(6 choose 5) = 6
+6 = 6
+The value of X is 2.
+
+Question: If $x - y = X$ and $x + y = 6$, The value of $y$ is -3. What is the value of unknown variable $X$?
+A: Let's think step by step.
+We are given that x - y = X and x + y = 6. We also know that y is equal to -3.
+We need to find the value of X, which represents the difference between x and y.
+To solve this, we can add the two given equations together:
+(x - y) + (x + y) = X + 6
+Simplifying the left side gives us:
+2x = X + 6
+To isolate X, we can subtract 6 from both sides of the equation:
+2x - 6 = X
+Since we know that y is equal to -3, we can substitute it into the equation x + y = 6:
+x + (-3) = 6
+Simplifying gives us:
+x - 3 = 6
+To solve for x, we can add 3 to both sides of the equation:
+x = 6 + 3
+x = 9
+Now we can substitute the value of x into the equation 2x - 6 = X:
+2(9) - 6 = X
+18 - 6 = X
+12 = X
+The value of X is 12.
+
+Question: The sum of the first $X$ odd positive integers is 100. What is the value of unknown variable $X$?
+A: Let's think step by step.
+We are given that the sum of the first X odd positive integers is 100.
+The sum of the first X odd positive integers can be calculated using the formula:
+Sum = X^2
+We need to find the value of X that makes the sum equal to 100.
+Setting up the equation:
+X^2 = 100
+To solve for X, we can take the square root of both sides of the equation:
+sqrt(X^2) = sqrt(100)
+Simplifying gives us:
+X = 10
+The value of X is 10.
+
+Question: The sum of two numbers is $X$. Their difference is $4$. The larger of the two numbers is 17. What is the value of unknown variable $X$?
+A: Let's think step by step.
+We are given that the sum of two numbers is X and their difference is 4. We also know that the larger of the two numbers is 17.
+Let's denote the two numbers as A and B, where A is the larger number.
+From the given information, we can set up two equations:
+A + B = X (equation 1)
+A - B = 4 (equation 2)
+We know that A is equal to 17, so we can substitute it into equation 2:
+17 - B = 4
+To solve for B, we can subtract 17 from both sides of the equation:
+-B = 4 - 17
+-B = -13
+Multiplying both sides by -1 gives us:
+B = 13
+Now we can substitute the value of B into equation 1 to find X:
+A + 13 = X
+Substituting A = 17, we get:
+17 + 13 = X
+30 = X
+The value of X is 30.
\ No newline at end of file

code_for_generating_data/configs/sv_rewrite_question_prompt_gsm8k.txt

+You are an AI assistant to help me rewrite question into a declarative statement when its answer is provided.
+Follow the given examples and rewrite the question.
+
+Question: How many cars are in the parking lot? The answer is 5.
+Result: There are 5 cars in the parking lot.
+
+Question: How many trees did the grove workers plant today? The answer is 6.
+Result: The grove workers planted 6 trees today.
+
+Question: If they ate 35, how many pieces do they have left in total? The answer is 39.
+Result: They have 39 pieces left in total if they ate 35.
+
+Question: How many lollipops did Jason give to Denny? The answer is 8.
+Result: Jason gave 8 lollipops to Denny.
+
+Question: How many toys does he have now? The answer is 9.
+Result: He now has 9 toys.
+
+Question: How many computers are now in the server room? The answer is 29.
+Result: There are 29 computers now in the server room.
+
+Question: How many golf balls did he have at the end of wednesday? The answer is 33.
+Result: He had 33 golf balls at the end of Wednesday.
+
+Question: How much money does she have left? The answer is 8.
+Result: She has 8 money left.
\ No newline at end of file

code_for_generating_data/configs/sv_rewrite_question_prompt_math.txt

+You are an AI assistant to help me rewrite question into a declarative statement when its answer is provided.
+Follow the given examples and rewrite the question.
+
+Question: what is the largest possible value of $|x|+|y|$? The answer is \sqrt{2}.
+Result: The largest possible value of $|x| + |y|$ is \sqrt{2}.
+
+Question: How far has he hopped after five hops? The answer is \frac{211}{243}}.
+Result: He has hopped \frac{211}{243} after five hops.
+
+Question: What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+3$? The answer is 63\pi.
+Result: The area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+3$ is 63\pi.
+
+Question: what is the value of $a+d$? The answer is 0.
+Result: The value of $a+d$ is 0.
+
+Question: What is the smallest number of homework assignments necessary to earn a total of 25 homework points? The answer is 75.
+Result: The smallest number of homework assignments necessary to earn a total of 25 homework points is 75.
+
+Question: What is the value of $n/p?$? The answer is 8.
+Result: The value of $n/p$ is 8.
+
+Question: Expand $(2z^2 + 5z - 6)(3z^3 - 2z + 1)$. The answer is 6z^5+15z^4-22z^3-8z^2+17z-6}.
+Result: The expansion of $(2z^2 + 5z - 6)(3z^3 - 2z + 1)$ is $6z^5 + 15z^4 - 22z^3 - 8z^2 + 17z - 6$.
+
+Question: Find the mean of all solutions for $x$ when $x^3 + 3x^2 - 10x = 0$. The answer is -1.
+Result: The mean of all solutions for $x$ when $x^3 + 3x^2 - 10x = 0$ is -1.
\ No newline at end of file

data/README.md

+# MetaMathQA Data
+
+## Train Data
+The full **MetaMathQA** dataset is now released in the huggingface [MetaMathQA](https://huggingface.co/datasets/meta-math/MetaMathQA/tree/main)!
+
+## Test Data
+We released the GSM8K_Backward dataset is also released in the huggingface [GSM8K_Backward](https://huggingface.co/datasets/meta-math/GSM8K_Backward) to evaluate the reversal mathematical reasoning ability!