Average Error: 0.1 → 0.1
Time: 7.4s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x \cdot x}{6} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x \cdot x}{6} - \frac{3}{6}
double f(double x) {
        double r41495 = x;
        double r41496 = r41495 * r41495;
        double r41497 = 3.0;
        double r41498 = r41496 - r41497;
        double r41499 = 6.0;
        double r41500 = r41498 / r41499;
        return r41500;
}
↓
double f(double x) {
        double r41501 = x;
        double r41502 = r41501 * r41501;
        double r41503 = 6.0;
        double r41504 = r41502 / r41503;
        double r41505 = 3.0;
        double r41506 = r41505 / r41503;
        double r41507 = r41504 - r41506;
        return r41507;
}

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 div-sub0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))