###### Abstract
To evaluate the performance and efficiency of inference, several key factors relating to the various stages of the process have to be taken into consideration and quantified. These factors are discussed in the following section. Various inference models have been proposed to assess the performance of AI tools [28; 29; 30], but there is no standard metric for evaluating the effectiveness of inferences across tasks and applications [31; 32]. This study introduces a new Inference Index (InI) methodology for assessing code-writing with LLMs, labeled the Inference Index In Testing Model Effectiveness (INFINITE). This methodology differs from other approaches due to its unique holistic approach to analyzing and quantifying the effects of key factors that impact the model's performance. This multidimensional assessment provides a richer picture of inference effectiveness and offers actionable insights into technical and operational aspects of deploying LLMs in code-generation tasks. Utilizing the INFINITE framework, we assess the coding abilities of different LLMs [1; 2]. To systematically evaluate their performance, we employ a two-step approach. First, we task the models with a fundamental code generation task: reading a CSV file, cleaning it by removing empty cells and NaN values, saving the cleaned data set in a new file, and computing the mean, median, and standard deviation for each column, storing these statistics in a separate text file. The results of this task are compared against a reference implementation developed by the authors to ensure correctness and reliability. Subsequently, we present the models with a more complex challenge--generating functional code for a Long Short-Term Memory (LSTM) model [33] to forecast meteorological variables. We compare the performance of ChatGPT-4o (GPT), OpenAI-o1 pro (OAI1), and OpenAI-o3 mini-high (OAI3) in executing these tasks, benchmarking their generated LSTM implementations against both observed data and predictions from an LSTM model developed by the authors (LSTM-H). Please note that all three software packages--GPT, OAI1 and OAI3--are developed and maintained by OpenAI, San Francisco, CA, USA. By evaluating both an easy and a complex problem, we ensure that the INFINITE framework is tested under different difficulty levels, providing a more robust assessment of its applicability. This study specifically focuses on OpenAI models to evaluate their code-generation capabilities and compare the performance differences between their paid and free versions. The choice to limit our comparison to OpenAI models was made to ensure a controlled and focused evaluation, avoiding variability introduced by architectural differences across different LLM providers. While other models such as Claude, Gemini, and LLaMA [34; 35; 36] may offer additional insights, their inclusion requires a more extensive comparative analysis that extends beyond the scope of this work. Our primary aim is to establish a clear understanding of how OpenAI models perform under different access conditions. However, we acknowledge the value of a broader comparison and plan to incorporate multiple LLM providers in future research to assess their relative performance in code generation. The paper is organized as follows: Section 2 introduces the INFINITE methodology. Section 3 briefly presents the LSTM model. In Section 4, an overview of the meteorological data set used in this study is provided. Section 5 describes the initial evaluation, where the models perform a fundamental data processing task--cleaning a CSV file, handling missing values, and computing basic statistical metrics--compared against a reference implementation, with results and analysis included. Section 6 then presents the more complex challenge of generating an LSTM model for forecasting meteorological variables, along with a discussion of the models' performance in this task. Finally, Section 7 reviews the findings and explores potential future directions.