Average Error: 0.2 → 0.2
Time: 1.1s
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 r69449 = x;
        double r69450 = r69449 * r69449;
        double r69451 = 3.0;
        double r69452 = r69450 - r69451;
        double r69453 = 6.0;
        double r69454 = r69452 / r69453;
        return r69454;
}
↓
double f(double x) {
        double r69455 = x;
        double r69456 = r69455 * r69455;
        double r69457 = 6.0;
        double r69458 = r69456 / r69457;
        double r69459 = 3.0;
        double r69460 = r69459 / r69457;
        double r69461 = r69458 - r69460;
        return r69461;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{x \cdot x - 3}{6}\]
  2. Using strategy rm

  3. Applied div-sub0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))