Average Error: 0.1 → 0.1
Time: 11.6s
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 r77495 = x;
        double r77496 = r77495 * r77495;
        double r77497 = 3.0;
        double r77498 = r77496 - r77497;
        double r77499 = 6.0;
        double r77500 = r77498 / r77499;
        return r77500;
}
↓
double f(double x) {
        double r77501 = x;
        double r77502 = 6.0;
        double r77503 = r77501 / r77502;
        double r77504 = r77503 * r77501;
        double r77505 = 3.0;
        double r77506 = r77505 / r77502;
        double r77507 = r77504 - r77506;
        return r77507;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{x \cdot x - 3}{6}\]
  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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))