Average Error: 0.1 → 0.2
Time: 7.1s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{1}{6 \cdot \frac{1}{x \cdot x - 3}}\]
\frac{x \cdot x - 3}{6}
↓
\frac{1}{6 \cdot \frac{1}{x \cdot x - 3}}
double f(double x) {
        double r86097 = x;
        double r86098 = r86097 * r86097;
        double r86099 = 3.0;
        double r86100 = r86098 - r86099;
        double r86101 = 6.0;
        double r86102 = r86100 / r86101;
        return r86102;
}
↓
double f(double x) {
        double r86103 = 1.0;
        double r86104 = 6.0;
        double r86105 = x;
        double r86106 = r86105 * r86105;
        double r86107 = 3.0;
        double r86108 = r86106 - r86107;
        double r86109 = r86103 / r86108;
        double r86110 = r86104 * r86109;
        double r86111 = r86103 / r86110;
        return r86111;
}

Error

Bits error versus x

Try it out

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 clear-num0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{6}{x \cdot x - 3}}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))