What does this equation mean?

A second, independently run measurement effort took a different approach: instead of asking whether an agent could solve one fixed set of tasks, it asked how long a task an agent could complete autonomously with 50% reliability, using human professional completion time as the unit. METR’s March 2025 study, compiled from 170 tasks and more than 800 human timing baselines across software engineering, cybersecurity and general reasoning work, reported that this “50%-task-completion time horizon” for frontier agents had been doubling approximately every seven months for six years running, and that the finding was robust to an order-of-magnitude error in the underlying measurements, which would only shift the projected timeline by around two years [ 14 ] . Writing the trend as a simple exponential makes its shape explicit: $T_{50}(t) \;=\; T_0 \cdot 2^{\,(t - t_0)/\tau}, \qquad \tau \approx 7 \text{ months}$. where $T_{50}(t)$ is the length of task, measured in human-hours, that a frontier agent could complete autonomously with 50% reliability at time t . This is an empirical regression over six years of a specific evaluation methodology, not a law of nature, and METR’s own reporting is explicit that the trend could bend in either direction; it is included here because it is the clearest available answer to “how would you know if agentic coding tools were actually getting more autonomous,” as distinct from “how would you know if a vendor said so.”