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  "body": "\n## Summary\n\nAffine arithmetic is a method of range analysis that represents each uncertain quantity as an affine function of shared noise symbols, each ranging over $[-1, 1]$.\nBecause quantities that depend on the same source of error share a noise symbol, their correlations are kept.\nThis avoids much of the overestimation of [[interval arithmetic|QPKKTE1ZY0]], where $x - x$ for $x \\in [0, 1]$ gives $[-1, 1]$ instead of $0$.\nNonlinear operations are approximated by affine ones, and the approximation error becomes a new noise symbol, so the bounds remain guaranteed.\n\n## Explanations\n\n### L1 human\n\nSuppose one only knows that a quantity $x$ lies between $1$ and $3$.\nInterval arithmetic forgets where a range came from, so it treats $x$ and a second copy of $x$ as unrelated, and $x - x$ seems to lie anywhere between $-2$ and $2$.\nAffine arithmetic writes $x = 2 + \\varepsilon$ with an unknown $\\varepsilon \\in [-1, 1]$, and keeps the same $\\varepsilon$ wherever $x$ appears.\nThen $x - x = 0$ exactly, and sums such as $x + 2x = 6 + 3\\varepsilon$ also come out sharp.\n",
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