PYTHON · NUMPY

The miss pays twice

A router is right 79.9% of the time. Make the typed model and its readout free. Best saving now?

Derive the ceiling a router imposes on any relocation saving, and read published claims backwards through it.

01Challenge

A typed model answers without generating. Route a decision to it, get it wrong, and you have paid for the typed pass and still owe the generated answer. Find what that does to the saving.

Predict firstA router is right 79.9% of the time. Make the typed model and its readout free. Best saving now?

02Model

Write the composed cost and the shape falls out. You pay the typed pass, you pay to read its answer back, and on every miss you pay the generative fallback too. Now let the typed pass and the readout go to zero, the most generous assumption anyone could make about a model. The saving does not go to infinity. It goes to one over one minus p. That ceiling is set by the router before a model is chosen, and nothing behind the router can lift it.

03Guided practice

Write the composed cost first. Take the limit as the typed cost goes to zero and read off the ceiling. Then invert it: given a claimed saving, what accuracy does the router need?

04Feedback

PASS WHEN You showed a 0.799 router caps the saving near 5x, and that the published 100x and 444.6x claims require 99.00% and 99.78% accuracy.

If your run fails, check:

The ceiling depends on the router and nothing else.
A cheaper typed model cannot buy you past one over one minus p.

05Retrieve & space

Why can making the typed model free not raise the ceiling?
A vendor claims 100x. What have they assumed about routing, without saying so?

06Mastery & project

You can convert any claimed saving into the routing accuracy it silently requires.

Find a published cost-reduction claim for a decision system. State the router accuracy it requires, and whether its authors report one.

GO FURTHER · THE LIVE PLAYGROUND

What a decision costs: the instrument ↗ · Move the router and watch the ceiling move with it.
PAI-350 · Reading an Energy Claim ↗ · The same inversion, applied to a thermodynamic claim.

← What generating an answer costs The decision that stays on the machine →

PYTHON · NUMPY

The miss pays twice

One identity in both directions. Forwards it gives the saving; backwards it gives the accuracy a published claim is quietly assuming.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you