Average Error: 0.2 → 0.1
Time: 18.1s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x}{\frac{6}{x}} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x}{\frac{6}{x}} - \frac{3}{6}
double f(double x) {
        double r56991 = x;
        double r56992 = r56991 * r56991;
        double r56993 = 3.0;
        double r56994 = r56992 - r56993;
        double r56995 = 6.0;
        double r56996 = r56994 / r56995;
        return r56996;
}
↓
double f(double x) {
        double r56997 = x;
        double r56998 = 6.0;
        double r56999 = r56998 / r56997;
        double r57000 = r56997 / r56999;
        double r57001 = 3.0;
        double r57002 = r57001 / r56998;
        double r57003 = r57000 - r57002;
        return r57003;
}

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-sub0.1

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

  4. Simplified0.1

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

  6. Applied associate-*l/0.1

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

  8. Applied associate-/l*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))