Computational models of reinforcement learning (RL) have significantly contributed to our understanding of human behavior and decision-making. Traditional RL models, however, often adopt a linear approach to updating reward expectations, potentially oversimplifying the nuanced relationship between human behavior and rewards. To address these challenges and explore models of RL, we utilized a method of model discovery using equation discovery algorithms. This method, currently used mainly in physics and biology, attempts to capture data by proposing a differential equation from an array of suggested linear and nonlinear functions. Using this method, we were able to identify a model of RL which we termed the Quadratic Q-Weighted model. The model suggests that reward prediction errors obey nonlinear dynamics and exhibit negativity biases, resulting in an underweighting of reward when expectations are low, and an overweighting of the absence of reward when expectations are high. We tested the generalizability of our model by comparing it to classical models used in nine published studies. Our model surpassed traditional models in predictive accuracy across eight out of these nine published datasets, demonstrating not only its generalizability but also its potential to offer insights into the complexities of human learning. This work showcases the integration of a behavioral task with advanced computational methodologies as a potent strategy for uncovering the intricate patterns of human cognition, marking a significant step forward in the development of computational models that are both interpretable and broadly applicable.