Average Error: 0.1 → 0.1
Time: 10.7s
Precision: 64
\[\frac{x \cdot x - 3.0}{6.0}\]
↓
\[x \cdot \frac{x}{6.0} - \frac{3.0}{6.0}\]
\frac{x \cdot x - 3.0}{6.0}
↓
x \cdot \frac{x}{6.0} - \frac{3.0}{6.0}
double f(double x) {
        double r4078604 = x;
        double r4078605 = r4078604 * r4078604;
        double r4078606 = 3.0;
        double r4078607 = r4078605 - r4078606;
        double r4078608 = 6.0;
        double r4078609 = r4078607 / r4078608;
        return r4078609;
}
↓
double f(double x) {
        double r4078610 = x;
        double r4078611 = 6.0;
        double r4078612 = r4078610 / r4078611;
        double r4078613 = r4078610 * r4078612;
        double r4078614 = 3.0;
        double r4078615 = r4078614 / r4078611;
        double r4078616 = r4078613 - r4078615;
        return r4078616;
}

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

    \[\frac{x \cdot x - 3.0}{6.0}\]
  2. Using strategy rm

  3. Applied div-sub0.1

    \[\leadsto \color{blue}{\frac{x \cdot x}{6.0} - \frac{3.0}{6.0}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.1

    \[\leadsto \frac{x \cdot x}{\color{blue}{1 \cdot 6.0}} - \frac{3.0}{6.0}\]

  6. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{x}{6.0}} - \frac{3.0}{6.0}\]

  7. Simplified0.1

    \[\leadsto \color{blue}{x} \cdot \frac{x}{6.0} - \frac{3.0}{6.0}\]

  8. Final simplification0.1

    \[\leadsto x \cdot \frac{x}{6.0} - \frac{3.0}{6.0}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))