Bandwidth-tunable filters are essential in elastic optical networks for dynamic bandwidth allocation. Existing solutions in silicon photonics face challenges to meet requirements in real-world applications due to design trade-offs and fabrication errors. In this Letter, we propose and experimentally demonstrate a silicon photonic tunable add-drop filter in a single-stage, hyperbolic-tangent-apodized contra-directional coupler with a segmented microheater. It allows to create an arbitrary temperature profile along the device for bandwidth tuning in both through and drop responses. We show that the algorithmic operation of the device can effectively compensate local fabrication nonuniformity and improve the out-of-band suppression ratio by 69%. Applying proper temperature offsets and slopes allows to continuously tune the filter's center wavelength over 8 nm and its drop-port 3 dB bandwidth between 14.0 and 22.4 nm.