Average Error: 0.1 → 0.1
Time: 11.8s
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 r4017312 = x;
        double r4017313 = r4017312 * r4017312;
        double r4017314 = 3.0;
        double r4017315 = r4017313 - r4017314;
        double r4017316 = 6.0;
        double r4017317 = r4017315 / r4017316;
        return r4017317;
}
↓
double f(double x) {
        double r4017318 = x;
        double r4017319 = 6.0;
        double r4017320 = r4017318 / r4017319;
        double r4017321 = r4017318 * r4017320;
        double r4017322 = 3.0;
        double r4017323 = r4017322 / r4017319;
        double r4017324 = r4017321 - r4017323;
        return r4017324;
}

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 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))