how a GPU improves battery life — E = P·t, race to idle, fixed-function offload (and the drain caveat)
Theorem.how a GPU improves battery life — E = P·t, race to idle, fixed-function offload (and the drain caveat).
Proof.how a GPU improves battery life, decoded completely (user, 2026-07-25: "how can gpu improve battery live?" · "all without gaps"). Battery drain is E = P·t (the time-integral of power), so the battery holds ENERGY not power and a higher-power part can still save energy if it finishes sooner. A GPU saves iff its SPEEDUP exceeds its POWER RATIO — race to idle: at 5× speedup and 5/3× power it uses only 1/3 of the CPU energy. The BIGGEST win is the dedicated fixed-function blocks (video decoders, ISP, compositor), ~10-100× more efficient per operation (~1/45 of the CPU energy in the model) — hardware-decoded playback lasts hours. And, WITHOUT A GAP, the failure mode: a wasteful GPU that does not race to idle (uncapped frame rates, always-on compute, rendering unseen frames) runs as long at higher power → 5/3 of the CPU energy, so it DRAINS. Therefore "GPU improves battery" is CONDITIONAL on offloading to the right engine, racing to idle, and capping frame rate (DVFS/power-gating help). SCOPE: a model over the energy identity and real hardware efficiency, dimensionless ratios normalised to the CPU baseline, NOT a device measurement. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/fire/physics/index.ts#gpuImprovesBatteryLifeByRaceToIdleAndFixedFunctionOffload
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"how a GPU improves battery life — E = P·t, race to idle, fixed-function offload (and the drain caveat)" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation gpuImprovesBatteryLifeByRaceToIdleAndFixedFunctionOffload.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (gpuImprovesBatteryLifeByRaceToIdleAndFixedFunctionOffload @ src/fire/physics) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes gpuImprovesBatteryLifeByRaceToIdleAndFixedFunctionOffload (src/fire/physics/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.