The emergence of ultra-large screening libraries, filled to the brim with billions of readily available compounds, poses a growing challenge for docking-based virtual screening. Machine learning (ML)-boosted strategies like the tool HASTEN combine rapid ML prediction with the brute-force docking of small fractions of such libraries to increase screening throughput and take on giga-scale libraries. In our case study of an anti-bacterial chaperone and an anti-viral kinase, we first generated a brute-force docking baseline for 1.56 billion compounds in the Enamine REAL lead-like library with the fast Glide high-throughput virtual screening protocol. With HASTEN, we observed robust recall of 90% of the true 1000 top-scoring virtual hits in both targets when docking only 1% of the entire library. This reduction of the required docking experiments by 99% significantly shortens the screening time. In the kinase target, the employment of a hydrogen bonding constraint resulted in a major proportion of unsuccessful docking attempts and hampered ML predictions. We demonstrate the optimization potential in the treatment of failed compounds when performing ML-boosted screening and benchmark and showcase HASTEN as a fast and robust tool in a growing arsenal of approaches to unlock the chemical space covered by giga-scale screening libraries for everyday drug discovery campaigns.