AI turns numerical-analysis intuition into Lean proofs with error bounds near 1e-48
geoffreyirving · x · 2026-10-15
Geoffrey Irving shares a concrete result: a Lean proof of a triple-double expansion approximation to exp with error bound |exp x − eˣ| ≤ (17/16·u³ + 2⁻¹⁶²)·eˣ + 3η ≈ 1.63×10⁻⁴⁸, where u = 2⁻⁵³ and η = 2⁻¹⁰⁷⁵, plus other transcendentals including a few from holomorphic dynamics.
In context of the thread: rigorous IEEE floating-point error bounds used to require enormous effort, but now "if you have a rough idea how the theory should go, you can translate that intuition into hard theory" — the gap between vague numerical-analysis intuition and formal proof has nearly vanished with very little work.
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