{
  "id": "2403.07492",
  "version": "v1",
  "published": "2024-03-12T10:30:46.000Z",
  "updated": "2024-03-12T10:30:46.000Z",
  "title": "P1 Error: A Combination of Absolute and Relative Errors",
  "authors": [
    "Peichen Xie"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We propose $\\frac{|x-y|}{1+|y|}$, termed the ``P1 error\" or ``plus-1 error\", as a metric of errors. It equals half the harmonic mean of absolute error and relative error, effectively combining their advantages while mitigating their limitations. The P1 error approaches absolute error when $|y|$ is small, and approaches relative error when $|y|$ is large. An $\\epsilon$ P1 error indicates that $x$ is close to $y$ at a tolerance level of $\\epsilon$, in compliance with the ``isclose\" definition used in popular numerical libraries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-12T10:30:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "p1 error approaches absolute error",
      "combination",
      "approaches relative error",
      "harmonic mean",
      "equals half"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}