Modern smartwatches often include photoplethysmographic (PPG) sensors to measure heartbeats or blood pressure through complex algorithms that fuse PPG data with other signals. In this work, we propose a collaborative inference approach that uses both a smartwatch and a connected smartphone to maximize the performance of heart rate (HR) tracking while also maximizing the smartwatch's battery life. In particular, we first analyze the trade-offs between running on-device HR tracking or offloading the work to the mobile. Then, thanks to an additional step to evaluate the difficulty of the upcoming HR prediction, we demonstrate that we can smartly manage the workload between smartwatch and smartphone, maintaining a low mean absolute error (MAE) while reducing energy consumption. We benchmark our approach on a custom smartwatch prototype, including the STM32WB55 MCU and Bluetooth Low-Energy (BLE) communication, and a Raspberry Pi3 as a proxy for the smartphone. With our Collaborative Heart Rate Inference System (CHRIS), we obtain a set of Pareto-optimal configurations demonstrating the same MAE as State-of-Art (SoA) algorithms while consuming less energy. For instance, we can achieve approximately the same MAE of TimePPG-Small (5.54 BPM MAE vs. 5.60 BPM MAE) while reducing the energy by 2.03x, with a configuration that offloads 80\% of the predictions to the phone. Furthermore, accepting a performance degradation to 7.16 BPM of MAE, we can achieve an energy consumption of 179 uJ per prediction, 3.03x less than running TimePPG-Small on the smartwatch, and 1.82x less than streaming all the input data to the phone.