Average Error: 0.2 → 0.1
Time: 1.1s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[x \cdot \frac{x}{6} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
x \cdot \frac{x}{6} - \frac{3}{6}
double f(double x) {
        double r84069 = x;
        double r84070 = r84069 * r84069;
        double r84071 = 3.0;
        double r84072 = r84070 - r84071;
        double r84073 = 6.0;
        double r84074 = r84072 / r84073;
        return r84074;
}
↓
double f(double x) {
        double r84075 = x;
        double r84076 = 6.0;
        double r84077 = r84075 / r84076;
        double r84078 = r84075 * r84077;
        double r84079 = 3.0;
        double r84080 = r84079 / r84076;
        double r84081 = r84078 - r84080;
        return r84081;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.2

    \[\frac{x \cdot x - 3}{6}\]
  2. Using strategy rm

  3. Applied div-sub0.2

    \[\leadsto \color{blue}{\frac{x \cdot x}{6} - \frac{3}{6}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.2

    \[\leadsto \frac{x \cdot x}{\color{blue}{1 \cdot 6}} - \frac{3}{6}\]

  6. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{x}{6}} - \frac{3}{6}\]

  7. Simplified0.1

    \[\leadsto \color{blue}{x} \cdot \frac{x}{6} - \frac{3}{6}\]

  8. Final simplification0.1

    \[\leadsto x \cdot \frac{x}{6} - \frac{3}{6}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))