step
0 / 60
Two numbers, 0.4 apart by less than a trillionth. Same rule, sixty steps each. Watch what a working-precision budget actually buys you.
The rule is xₓ₊ = 3.97·x₋(1−x₋): the same one that fooled a plain float64 loop into reporting a wrong "ground truth" in the field notes this simulates. Drag ε smaller and run again: the two lines stay glued together longer, but they still come apart by step 60. There's no ε small enough to fix this at fixed precision; only enough working precision, carried the whole way, buys a trustworthy answer. That's the whole finding, watchable instead of argued.