## 2 Inference and the INFINITE Methodology
* As a second step, we develop indices ranging from 0 to 1 which define the performance of each individual factor separately; 0 represents the poorest performance while 1 indicates excellent performance. * Finally, InI is calculated by weighting the average of individual indices. For the first step of the methodology, key parameters that can be recorded during the execution of a code-generating task include the number of different questions (attempts) we must ask the model until the correct code is produced, the number of queries that need to be submitted each time (whether an SB response or an answer is returned), response times between a query and the response from the framework, SB responses, and accuracy metrics, such as coefficient of determination R\({}^{2}\) or Mean Absolute Percentage Error (MAPE), between generated model predictions and ground truth. The SB responses, total number of queries, and response times are related to Efficiency. The number of questions posed until a satisfactory answer is achieved is tied to Consistency. The accuracy metrics correspond to Accuracy. In Figure 1, we visually present the three major components and their corresponding parameters. As we focus on code-generating tasks, we believe that metrics such as BLEU [45] or codeBLEU [46] are not well suited for evaluating the accuracy of these tasks; both metrics measure the number of contiguous sequences of words (or tokens) from a generated text that match those in a reference text, rather than assessing the degree of deviation in code correctness. In the context of code generation, n-gram similarity does not necessarily reflect correctness, functionality, or logical consistency. A piece of code may be syntactically similar to a reference implementation yet fail to execute correctly, while a semantically equivalent yet lexically different implementation may receive a lower BLEU score despite being correct. For this reason, our evaluation approach incorporates supervised assessment to ensure that correctness, execution validity, and logical consistency are properly accounted for through the use of MAPE or R\({}^{2}\) score. While this introduces some level of human involvement, it ensures that the generated code is not just similar but functionally correct. Future work can explore hybrid approaches that balance automation with correctness verification, allowing for more scalable yet reliable evaluations. As a second step, we offer suggestions for the indices that should be formulated to calculate InI. All indices range from 1 (excellent performance) to 0 (poorest performance). First, we consider both the SB rate and the \(ARTpQ\) for Efficiency. Therefore, two indices are formulated. We propose the SB rate to be represented through index \(E_{SBR}\):  
\[E_{SBR}=1-\frac{\text{Number of SB responses}}{\text{Total queries}} \tag{2}\]  
The greater the number of SB responses the framework returns, the poorer its performance becomes. To account for \(ARTpQ\), we define two threshold values of average response time, \(ART_{1}\) and \(ART_{2}\), where \(ART_{1}<ART_{2}\). Then, we define index \(E_{ART}\), such that the performance is excellent, average, or poor:  
\[E_{ART}= \begin{cases}1,&\text{if }ARTpQ\leq ART_{1}\quad\text{(Excellent performance)}\\ 0.5,&\text{if }ART_{1}<ARTpQ<ART_{2}\\ &\text{(Average performance)}\\ 0,&\text{if }ARTpQ\geq ART_{2}\quad\text{(Poor performance)}\end{cases}  \tag{3}\]  
The values for \(ART_{1}\) and \(ART_{2}\) depend on the user and the nature of the problem. We suggest reasonable values \(ART_{1}=10\)s and \(ART_{2}=30\)s.  
Then, index \(E\) for Efficiency may be derived from averaging the two indices \(E_{SBR}\) and \(E_{ART}\):  
\[E=\frac{E_{SBR}+E_{ART}}{2} \tag{4}\]  
To construct a well-balanced decay function for the Consistency index \(C\), we introduce \(ln(Q)\) instead of simply using \(Q\), where \(Q\) represents the total number of attempts (i.e., questions asked).