Batteryless IoT devices, powered by energy harvesting, face significant challenges in maintaining operational efficiency and reliability due to intermittent power availability. Traditional checkpointing mechanisms, while essential for preserving computational state, introduce considerable energy and time overheads. This paper introduces Approxify, an automated framework that significantly enhances the sustainability and performance of batteryless IoT networks by reducing energy consumption by approximately 40% through intelligent approximation techniques. \tool balances energy efficiency with computational accuracy, ensuring reliable operation without compromising essential functionalities. Our evaluation of applications, SUSAN and Link Quality Indicator (LQI), demonstrates significant reductions in checkpoint frequency and energy usage while maintaining acceptable error bounds.