Average Error: 0.2 → 0.1
Time: 1.3s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x}{6} \cdot x - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x}{6} \cdot x - \frac{3}{6}
double f(double x) {
        double r44704 = x;
        double r44705 = r44704 * r44704;
        double r44706 = 3.0;
        double r44707 = r44705 - r44706;
        double r44708 = 6.0;
        double r44709 = r44707 / r44708;
        return r44709;
}
↓
double f(double x) {
        double r44710 = x;
        double r44711 = 6.0;
        double r44712 = r44710 / r44711;
        double r44713 = r44712 * r44710;
        double r44714 = 3.0;
        double r44715 = r44714 / r44711;
        double r44716 = r44713 - r44715;
        return r44716;
}

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 associate-/l*0.1

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

  7. Applied associate-/r/0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))