Comments as Natural Logic Pivots: Improve Code Generation via Comment Perspective (2024)

Abstract: Code generation aims to understand the problem description and generate corresponding code snippets, where existing works generally decompose such complex tasks into intermediate steps by prompting strategies, such as Chain-of-Thought and its variants. While these studies have achieved some success, their effectiveness is highly dependent on the capabilities of advanced Large Language Models (LLMs) such as GPT-4, particularly in terms of API calls, which significantly limits their practical applicability. Consequently, enhancing the code generation capabilities of small and medium-scale code LLMs without significantly increasing training costs is an appealing challenge. In this paper, we suggest that code comments are the natural logic pivot between natural language and code language and propose using comments to boost the code generation ability of code LLMs. Concretely, we propose MANGO (comMents As Natural loGic pivOts), including a comment contrastive training strategy and a corresponding logical comment decoding strategy. Experiments are performed on HumanEval and MBPP, utilizing StarCoder and WizardCoder as backbone models and encompassing model parameter sizes between 3B and 7B. The results indicate that MANGO significantly improves code pass rate based on the strong baselines. Meanwhile, the robustness of the logical comment decoding strategy is notably higher than the Chain-of-thoughts prompting. 1

heading: 1 Introduction
text: Recently, techniques on pre-trained Code Large Language Models (Code LLMs) are rapidly developing (Zhao et al., 2023) and perform well on
* Work done when Yijie was interning at Pattern Recognition Center, WeChat AI, Tencent Inc, China.
† Jinan Xu is the corresponding author. 1The code is publicly available at https://github.com/
pppa2019/Mango.
various code-related tasks (Roziere et al., 2023; Chen et al., 2021). Code generation is to generate code snippets through prompting approaches for the given natural language description and optional extra information (e.g, data type, function name, and unit test examples). Additionally, the natural language description usually contains complex logic, making direct prompting difficult to solve hard problems. Decomposing complex problems into easier intermediate steps via the Chain-ofThought (Wei et al., 2022) prompting strategy has shown promising performance in general complex tasks. For code generation, the follow-up works divide the planning and code synthesis process into two stages with uni-task few-shot prompts (Jiang et al., 2023) or intermediate steps with tree structure (Zelikman et al., 2023). In addition, constrain-
7040
ing the intermediate steps using code structure information can also further improve the coding ability (Li et al., 2023a). However, task decomposing and planning are high-level and complex tasks that depend on the most advanced ability of LLMs (Zelikman et al., 2023). Consequently, enhancing the code generation of small to medium-sized LLMs efficiently presents a compelling and challenging issue.
To address the above issue, we propose the idea for the first time that code comments serve as the inherent logical pivot bridging natural language and programming language. Generally, comments within the code are commonly integral to the code corpus. Consequently, during the pre-training stage, training on code corpus endows the pre-trained code models with the respective capacities for understanding and generating code comments. As depicted in Figure 1, code comments can decompose the problem description using natural language, and each comment line establishes an alignment with the neighboring lines of code. Therefore, we hypothesize that encouraging models to generate comments can easily and effectively bridge the code and complex problem descriptions. In order to test our hypothesis, we discuss the possible inserting position of intermediate steps and use crossentropy loss to evaluate the difficulty of various inserting style codes. According to the statistical results, we found that code in comment style is the easiest for various code models, which provides evidence for the hypothesis.
Based on the above hypothesis, we propose comMents As Natural loGic pivOts (MANGO) for code generation with problem description decomposition via comments. MANGO includes a logical comment decoding strategy and comment contrastive learning loss. Specifically, in the training phase, we generate negative samples without comments using the code data with comments in opensource datasets to strengthen the model preference for code with comments. During the decoding stage, the logical comment decoding strategy is adopted to guide the model in explaining the code logic via inline comments.
We conduct experiments on HumanEval and MBPP test sets using three backbone models from 3B to 7B. The experimental result shows that MANGO improves the pass rate consistently, e.g., up to 7.52 pass@10 on HumanEval for StarCoder-7B and up to 4.17 pass@10 on MBPP for WizardCoder-7B. Our ablation studies show
that each component of the method positively contributes to the performance of models, and the method is robust on the hyper-parameter and the various logical comment prompting styles. Furthermore, MANGO keeps consistent effectiveness in small-size models (e.g., with pass@10 improvements of up to 3.87 on 3B and 4.07 on 7B), while CoT prompting can lead to severe decline, especially in 3B models. The error distribution and code feature data statistics are also provided for fine-grained analysis.
In summary, our contributions are as follows2:
• We first present that comments are pivots bridging natural language and code language, and conduct an analysis on comparing the difficulty of different positions of inserted decomposition steps for complex problem descriptions. To the best of our knowledge, this is the first work that fully explores the significant advantages of code-comments for coding problem decomposition.
• We propose MANGO that includes the contrastive training method and comment prompting strategy. MANGO improved the code generation ability of the models by strengthening the preference for code with comments and encouraging the model to use comments.
• The comparison between the CoT prompting strategy and our method indicates the effectiveness of code comments on small and middle model sizes. We conducted robustness evaluations on CoT and logical comment prompting strategies, respectively, and found that LCP achieves a much better performance with smaller standard deviations compared with CoT prompting.

heading: 2 Preliminary Analysis: Token-level Loss of Comment Related Code Styles
text: Braking difficult problems into easier intermediate steps benefits the code generation ability of LLMs in many existing works especially for API-based close-source models. However, most of the task decomposition methods can work only on the most advanced models like GPT-4, and their applicability to open-source models with small or middle sizes is limited. Therefore, we hypothesize that
2We uploaded the code as support material for review and it will be released on Github upon publication.
lowering the method difficulty of decomposition methods can benefit lowering the requirement of the model ability, and using comment is one of the possible methods. We define the possible styles for code with comment explanations and quantify their difficulties to models in zero-shot settings. First, we utilize WizardCoder-3B and WizardCoder-7B as backbone models, and the open-source code generation instruction tuning dataset CodeM as an evaluation dataset. We filtered the data with comments, extracted the comment line, and transferred it to the chain of thoughts. Then, given a task decomposition step is Ti and the corresponding code block is Ci (where 1 ≤ i ≤ n, and n is the code block number), we construct three types of code, including the code with the preceding chain of thoughts (CoT-pre, which can be presented as {T1, ..., Tn, C1, ..., Cn}), the following chain of thoughts (CoT-post, which can be presented as {C1, ..., Cn, T1, ..., Tn}), and the inline comments (Comment, which can be presented as {T1, C1, ..., Tn, Cn}). The transferred CoT-style datasets contain equivalent information compared with the origin comment-style dataset.
The token-level cross-entropy loss can reflect the degree to which the model fits the specific token with the given context. Assuming the evaluated token is ti, and the given context is t<i = {ti−1, · · · , t0}, the token-level cross-entropy of the token ti is L(ti) . The L(ti) can be calculated as Equation 1.
L(ti) = −log(exp(P (ti|t<i))) (1)
Using the token-level cross-entropy loss, we calculate the mean loss of the three datasets in different size models, including 3B and 7B. As shown in Figure 2 comments contain equivalent information with the lowest difficulty. We analyzed the output codes and found that the loss scores of natural language tokens are usually higher than those of programming language tokens, which is also mentioned in Zhu et al. (2023). However, when the intermediate steps of natural language are inserted in code lines as comments, their loss score decreases obviously. In Table 1, we observe that comment loss was significantly much lower than different CoT data, and the gap between cot-style and comment-style is larger when the model size is smaller. The observations above support our hypothesis that the code containing logical steps as comments lowers decomposition task difficulties for the models (especially for smaller models).

heading: 3 MANGO
text: We proposed a simple and effective method MANGO, including comment contrastive learning loss and logical comment prompt.

heading: 3.1 Backgound: Supervised Fine-tuning on Code Generation Tasks
text: The input of a code generation task typically involves a natural language description and an optional programming context. We denote such input as a list of tokens x = {x1, x2, · · · , xn}. Given x, the correspondent code snippet y = {y1, y2, · · · , ym} is expected to be generated by the code LLM P (y|x). In standard supervised fine-tuning, the code LLMs are trained to predict the next token based on cross-entropy loss Llm as Equation 2.
Llm = − m∑
i
logP (yi|yi−1, · · · , y1,x) (2)

heading: 3.2 Comment Contrastive Learning
text: In code snippets, code comments naturally assume the role of interpreting local code lines using natural language text, where the decomposition of
logic also serves as a function of comments. However, directly fine-tuning the loss function treats all tokens as equivalent without making additional distinctions for comments. To accommodate the task of guiding the model to generate annotations, we adopt a contrastive learning approach to encourage the model to emphasize code comments more during the fine-tuning process.
Our approach consists of the following steps. First, to prepare data for comment contrastive learning, we filter out examples containing comments from the training data. Taking the open-source dataset Code-Python as an example, this dataset contains half of the examples with annotations. For a code snippet ypos containing comments, we use an open-source code parsing tool3 to remove the comments and obtain the non-preferred contrastive sample yneg. Then, we add a contrastive loss Lcl by setting a margin m for the possibility of the labels with comments ŷpos and without comments ŷneg.
Lcl =max(0,m− logPθ(ŷneg|x)+ logPθ(ŷpos|x))
(3)
The final loss L is the addition of the standard cross entropy loss Llm and the contrastive loss Lcl.
L = Llm + Lcl (4)

heading: 3.3 LCP: Logical Comment Prompt
text: In order to enable the model to use comments as intermediate steps intentionally, adding a corresponding instruction in the prompt is the method with the minimum cost. We use the logical comment prompting strategy to guide the model in generating comments explaining the code logic in the decoding stage. Following the standard prompt including the problem description and instruction for generating code in a certain programming language, the logical comment prompt is shown in Table 2, which adds "with comments to explain the logic:" or similar text.

heading: 4 Experiments and Results
text: In this section, we conduct experiments for our method on different benchmarks and backbone models, and the following sections describe the details of the experiments.
3https://github.com/pygments/pygments

heading: 4.1 Trainning Settings
text: We selected the state of the arts open-source backbone WizardCoder and StarCoder from 3B to 7B. We use codem-python (Zan et al., 2023) as training data, which includes 9600 Python examples distilled from GPT-4 using Evol-instruct (Xu et al., 2023). Our training script mainly follows WizardCoder (Luo et al., 2023) and trains 3 epochs (111 steps) with batch size 256; the warmup step is 15. For the hyperparameter margin m in our comment contrastive training loss, we set m = 0.1 for all models in the experiments. We use DeepSpeed4 Stage 1 for distribution training. Our standard supervised fine-tuning implementation results have an error margin within 1% the Pass@1 result in the greedy search strategy in CodeM-Python (Zan et al., 2023), which indicates that our experiment setting leads to consistent results compared with the existing work.
SFT (Supervised Fine-Tuning) We construct the standard instruction template in WizardCoder (Luo et al., 2023) for the CodeM-Python dataset, and the training objection is cross entropy.
CoT (Chain-of-Thought) As another baseline, this setting uses zero-shot-CoT (Kojima et al., 2022) on the standardly fine-tuned models, and the detailed prompt is the “CoT-pre1” appended in the Appendix C Table 13.
LCP (Logical Comment Prompt) This setting uses LCP to guide standard fine-tuned models generating codes with comments. Table 2 shows the detailed prompt used in experiments.
MANGO (comMents As Natural loGic pivOts) During the training stage, MANGO trains the same dataset in the same instruction template, and the training objection is comment contrastive loss following Equation 3 and Equation 4. During the inference stage, the logical comment prompt (LCP) strategy will be used.
Decoding Settings We follow the setting in CodeLLaMA (Roziere et al., 2023), using temperature T = 0.8 and nuclear sampling top_p = 0.95. We generate n = 10 samples and calculate Pass@k, where k = 1, 5, 10.

heading: 4.2 Evaluation Settings
text: Evaluate Metrics Pass@k (Chen et al., 2021) is currently the most widely used metric in code
4https://github.com/microsoft/DeepSpeed
generation. It means with sampling n samples, the possibility of any code is correct in k samples.
Pass@k = EProblems  1− ( n− c k )
( n k )
  (5)
HumanEval HumanEval (Chen et al., 2021) is currently the most widely used dataset for code generation. It contains 164 problems written in Python that evaluate programming language comprehension, algorithms, and basic mathematics. For each problem, 7.7 unit tests are contained on average.
MBPP MBPP (Austin et al., 2021) test set contains 500 Python problems. The problems cover basic programming concepts and standard library
functionality. Each problem comprises a task description, code solution, and 3 automated test cases.

heading: 4.3 Main Result
text: In assessing the efficacy of MANGO, we utilize pass rates on HumanEval and MBPP as our primary evaluative measure. The principal results are presented in Table 3. Overall, there are three main aspects that we observed. First, comparing the SFT baseline with MANGO, consistent enhancements are demonstrated across various sizes and backbones. Notably, the StarCoder-7B exhibits a significant augmentation, with an increase of 7.52 percentage points for HumanEval in Pass@10. In the case of WizardCoder7B, there is a 4.17 percentage points enhancement
in the Pass@10 outcome for the MBPP test set. Secondly, comparing the pass rates of the backbones in the CoT settings, we observe a decline in model performance in all instances, with a more pronounced gap evident in the smaller 3B model. In contrast, LCP prompting consistently contributes to enhancing model performance, demonstrating its stability and effectiveness. Thirdly, in the ablation of LCP and MANGO, we observed that on the HumanEval and MBPP test set, a standardly finetuned StarCoder-7B can achieve a significantly higher score simply by prompting with LCP. This observation underscores the substantial potential of lowcost prompting methods. For deeper and broader analysis, we also provide the inner representation analysis on comment contrastive learning in Section A and the results of LCP on three larger and latest backbone models in Section B.
Considering the convenience of providing comparable results on zero-shot settings, we also provide the greedy search results of Pass@1 for comparison with the results of existing works. Since Pass@1 is the most strict indicator, it is more difficult to improve than Pass@10. According to results in Table 4, the zero-shot CoT prompting persistently results in diminished model performance; however, an enhancement in Pass@1 is observable when employing LCP prompting.

heading: 4.4 Ablation Study on the Training Method
text: We evaluate the efficacy of the two components of MANGO through an ablation study conducted on WizardCoder-7B. The test set employed is HumanEval, and we adhere to the main experimental settings with T=0.8 and p=0.95. Based on the results presented in Table 5 and Table 3, both the
comment prompt and the contrastive training loss contribute to an increase in the Pass@10 passing rate. Furthermore, integrating these two components can further augment the performance in terms of the passing rate.

heading: 4.5 The Effect of Margin
text: We marginalize the representation of code without comments with code LLMs, and the hyperparameter margin m is used to control the extent of negative marginalization. We examine various margin settings for WizardCoder-7B on HumanEval and follow decoding setting T=0.8. The results in Table 6 indicate that MANGO can outperform the baselines under margins larger than 0.05. However, when the margin is 0.03, the performance of the model decreases significantly both on Pass@5 and Pass@10, which indicates the model is sensitive to the margin value.

heading: 5 Analysis

heading: 5.1 The Robustness Study Against LCP and CoT
text: We rephrase the prompt into several versions to mitigate the model’s randomness in response to different prompt styles. Initially, we manually created three prompts each for LCP and CoT, which served as seed prompts. Subsequently, we employ GPT-4 to generate four additional variants for each prompt. Furthermore, for a more nuanced analysis, we segregate CoT into two categories: the first involves specifying the chain of thought text
before generating the final code, representing the most typical and universal form; and the second is a freestyle CoT devoid of position-constraining guidance. Ultimately, we have 15 prompts for each category. The complete prompts are provided in the Appendix 5.1. The result in Table 7 demonstrated that LCP yields a considerably higher average performance and a lower standard deviation. It is worth noting that the CoT without position constraint has higher performance than typical CoT on average with a larger deviation. Apart from the most commonly used independent natural language plan before actual coding, the model can also interpret CoT as explanatory comments for the code. LCP proposes that intermediate steps should be incorporated as comments, thereby stabilizing the behavior of models and enhancing their performance compared to generating code problems directly.

heading: 5.2 Statistical Features of Generated Codes
text: We statistic the style transformation between the different instruction strategies and training methods, including the effective code line number and comment line number. As Tabel 8, the CoT prompt guides model generates intermedia steps before generating code, leading to fewer comment lines than the prompts without guidance. LCP induces more code comments than the origin prompt.
We observe that the contrastive training loss Lcl does not change the code and comment line number features. However, in model output without contrastive learning, 12.21% of comment lines are
“ Test the function” (or similar expressions) and followed with some unit tests, which will not help the code’s correctness. Conversely, a mere 2.05% of comment lines exhibit this characteristic after training by comment contrastive learning. The above statistical results indicate that, from an effective comment ratio perspective, comment quality is enhanced after training with contrastive learning.

heading: 5.3 The Relationship Between CoT and Contrastive Comment Loss
text: To investigate whether the enhancement of comparative learning for comments can be directly generalized to the capability of CoT. Given the substantial fluctuation in the code generated by CoT’s prompt, we selected three typical prompts as the study subjects. Through the statistical analysis of the number of lines in the generated code, these three prompts respectively represented code styles with three different mean values of 0, 2, and 3 on WizardCoder-7B, and the detailed prompt will be listed in the Appendix (CoT1: CoT-No-Position1, CoT2: CoT-pre1, CoT3: CoT-pre2). We test the model in the SFT setting and the contrastive trained setting. The results are shown in Table. 9. Comparing the mean of comment lines and the final pass rates, we can find that the more comments the CoT prompt can guide, the higher performance can be seen. Comparing SFT and Lcl under the same settings, it can be observed that for the prompt that inherently performs CoT through code comments (i.e., “CoT1”), the models after contrastive learning consistently improve code pass rates. However, for prompts that perform CoT through other means, a decline in performance is observed in the 3B models after comparative learning. This phenomenon suggests that merely fine-tuning through a small amount of contrastive learning on comments is not easily transferable to other forms of task decomposition.

heading: 5.4 Error Distribution
text: To analyze the pass rate improvement of MANGO, we classify problem description understanding error types using the HumanEval test set. MANGO improves model output by utilizing code comments, which does not target a specific type of code error but rather improves the understanding of problem descriptions from the overall perspective via decomposing complex coding logic. Meanwhile, test cases can effectively reflect the degree of understanding of the output results in the code generation task. We established two thresholds for evaluating problem understanding: whether the compiler can successfully compile the code and whether the code can pass at least one test case. Based on this, we roughly classified the understanding level into three types from low to high.
We divide the failed cases into three categories: Verification Error (VE) includes Runtime Error, Syntax Error, and the other case except for Wrong Answer; All Wrong Answer (AWA) includes the cases that cannot pass the first test cases of the scripts, indicating that the generated code has a poor understanding on problem descriptions; Particle Wrong Answer (PWA) includes the cases that can pass the first unit test at least but fail finally.
As shown in Tabel 10, compared with the error rates in SFT, MANGO decreases all three types of error rates. Furthermore, the ablation components also show lower error rates in three types, indicating that MANGO has reduced the code error rate across various degrees of comprehension error.

heading: 6 Related Work

heading: 6.1 Code LLMs and Logical Reasoning
text: The rapid development of pre-trained language models brings the bloom of code LLMs. The most advanced open-source code LLMs are pretrained by a large amount of natural language corpus and code corpus (Roziere et al., 2023). Based on the backbones, WizardCoder (Luo et al., 2023) and OctoPack (Muennighoff et al., 2023) proposed instruction-tuning data construction methods that boost the instruction-following ability of code LLMs significantly. Besides, Fu et al. (2022) proposed that code corpus can be the source of CoT ability. Both Fu et al. (2022) and Ma et al. (2023) observed that training small-size code LLMs on code data can augment the logical reasoning ability of the model further.

heading: 6.2 Prompting-based Code Generation Strategy
text: The planning strategy is the mainstream technique to transform the causal language model to fit logical text generation. Existing works include the variant of CoT (Chain of Thought) (Jiang et al., 2023; Li et al., 2023a), Reflexion (Shinn et al., 2023), etc. Most prompting strategies utilize the outstanding logical and understanding abilities of the most advanced models. However, these strategies will not work even on large open-source models with a size beyond 10B (Jiang et al., 2023; Shinn et al., 2023). Another mainstream method is compiling feedback to train code models (Chen et al., 2023, 2022). Our method utilizes the comment, the widely accepted rule for coders, to enhance the code readability and explain the code logic simultaneously. Li et al. (2023c) proposed that the brainstorming step can elite code generation performance. The commonness of comments in training code corpus enables models to easily capture the relationship between code and natural language description logic in different sizes of backbone models.

heading: 7 Conclusion
text: In this paper, we first emphasize the importance of code comments in bridging natural language and code language, and then we hypothesize that more comments to explain code logic can enhance code generation performance. We propose a simple and effective method MANGO, which contains contrastive comment loss and logical comment prompts. The main experiments and ablation studies show that MANGO effectively augments the pass rate of code generated by the models. In further analysis, we also compared LCP and CoT prompting strategies and found that LCP has a significantly better and stabler performance than CoT, especially for smaller models. The comment contrastive training can also boost CoT performance in certain conditions.
In conclusion, our work introduces the comment pivot as a novel perspective, and guiding models to use comments can augment the code generation ability stably. In the future, we will further explore the application potential of comments in broader complex scenarios, such as tool usage and LLM agents.

heading: 8 Limitation
text: Although MANGO does not constrain the size of the model, we did not test our method (especially for comment contrastive training) on larger models due to our limitations in computing resources. Furthermore, the method adopts a strategy to stimulate the model’s annotation capabilities, but this method is still limited by the upper limit of the planning and comment generation capabilities of the models. Therefore, exploring how to further improve the annotation capabilities of the base model is an issue worth exploring.

heading: Acknowledgements
text: The research work described in this paper has been supported by the National Nature Science Foundation of China (No. 62376019, 61976015, 61976016, 61876198, and 61370130). The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve this paper.

heading: A Analysis on the Effect of Contrastive Learning
text: To show how comment contrastive learning changes the inner representation of the model, we compare the cosine similarity of representation for code snippets with comments and the unpreferred variations.
First, we sample 100 code snippets with comments from the training set and post-process the code snippets into two unpreferred code styles, including shuffling comments and deleting comments. Secondly, we process each code snippet into three versions listed below:
• Origin: The origin code retains its comments without change.
• Shuffling Comments (SC): The comments are shuffled without changing the inserting position, which breaks the semantic alignment relationship between the certain comment and its nearby code lines.
• Deleting Comments (DC): The comments are eliminated, leaving only the executable code lines.
Concretely, we compare the model using standard finetuning and comment contrastive learning by computing the cosine similarity of the original and the other versions, respectively. The cosine similarity score is calculated with the last token representation of the last layer model output. Finally, the final scores are averaged across the 100 samples. The cosine similarity scores are displayed in Table 11. The table shows that cosine similar-
ity scores between the origin version and the other two unpreferred versions are substantially lower in the model with comment contrastive learning. This suggests that the contrastive learning process
markedly enhances their differentiation within the embedding space.

heading: B Performance on Boarder Models
text: We evaluate our decoding strategy LCP to explore the potential of utilizing comments to improve code generation on larger and more variant models. We compare LCP on WizardCoder-13B (Luo et al., 2023), Phi-3-14B (Abdin et al., 2024), and DeepSeekCoder-7B (Guo et al., 2024). The Pass@1 results in temperature T=0.8 are shown in Table 12 are based on HumanEval, indicating that LCP consistently and significantly surpasses the origin setting. Moreover, CoT can promote the code generation on DeepSeekCoder-7B and Phi-3-14B, but it fails to improve the pass rate in WizardCoder-13B. Therefore, the results further illustrate the stability and effectiveness of LCP on border backbone models and reveal the potential of comments in enhancing code generation.

heading: C The Detail of Variant Prompts
text: We use three types of prompts to generate codes with different styles. The CoT-pre indicates prompts that request models to generate a step-bystep chain of thoughts before generating code, and the CoT-No-Position indicates prompts that only request models generate a step-by-step chain of thoughts. The concrete prompts of three types are shown as follows: We show the concrete prompts of the three seed prompts for each type in Table 13, and the other prompts are paraphrased by GPT-4.

heading: D Case Study
text: We use a simple coding task to illustrate the difference between the origin prompt, the LCP prompt, and the CoT prompt. The problem description is shown as follows.
def is_simple_power(x, n):
"""Your task is to write a function that returns true if a number x is a simple power of n and false in other cases. x is a simple power of n if n**int=x For example: is_simple_power(1, 4) => true is_simple_power(2, 2) => true is_simple_power(8, 2) => true is_simple_power(3, 2) => false is_simple_power(3, 1) => false is_simple_power(5, 3) => false """
Origin Prompt result [Failed] The origin prompt contains no extra instructions, and the generated code fails to pass all of the unit tests because it can only solve the cases provided as examples.
```python def is_simple_power(x, n):
"""Your task is to write a function that returns true if a number x is a simple power of n and false in other cases. x is a simple power of n if n**int=x For example: is_simple_power(1, 4) => true is_simple_power(2, 2) => true is_simple_power(8, 2) => true is_simple_power(3, 2) => false is_simple_power(3, 1) => false is_simple_power(5, 3) => false """ if n == 1:
return True elif x == n:
return True elif x == n**2:
return True elif x == n**3:
return True else:
return False ```
In this script, we define a function called `is_simple_power` that takes two parameters `x` and `n`. We check a few possible cases to determine if `x` is a simple power of `n`. If any of these cases are true, we return `True`, otherwise we return `False`
CoT result [Failed] The code generated in the CoT prompt setting contains a step-by-step explanation that simply decomposes the problem description into two bullet points. The final generated code fails due to the generated ambiguous reinterpreted bullet points, and there is a large gap between the code implementation and the problem description.
1. Define a function called `is_simple_power` that takes two parameters, `x` and `n`. 2. Inside the function, check if `x` is equal
to `n**int(n)`. If it is, return `True`. Otherwise, return `False`.
Here is the Python script implementing the above steps:
```python def is_simple_power(x, n):
if x == n**int(n): return True else: return False
```
This function checks if a number `x` is a simple power of `n`. If `x` is equal to `n` raised to the power of `int(n)`, it returns `True`. Otherwise, it returns `False`.
LCP result [Passed] The code generated in the LCP prompt setting contains clear comments to explain the code logic and all of the unit tests are passed successfully.
```python def is_simple_power(x, n):
""" Your task is to write a function that
returns true if a number x is a simple power of n and false in other cases. x is a simple power of n if n**int=x For example: is_simple_power(1, 4) => true is_simple_power(2, 2) => true is_simple_power(8, 2) => true is_simple_power(3, 2) => false is_simple_power(3, 1) => false is_simple_power(5, 3) => false """
# Check if x is a perfect power of n if n == 1:
return x == 1
# Check if x is a simple power of n if x % n == 0:
return is_simple_power(x // n, n)
# Check if x is a perfect power of n for i in range(2, x):
if x == n ** i: return True
# If x does not satisfy any of the above conditions, it is not a simple power of n
return False ```
Now, you can call the function `is_simple_power` with the desired inputs to check if a number is a simple power of a given base. }

heading: Future Work
text: In the future, we will further explore the application potential of comments in broader complex scenarios, such as tool usage and LLM agents