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 r83237 = x;
        double r83238 = r83237 * r83237;
        double r83239 = 3.0;
        double r83240 = r83238 - r83239;
        double r83241 = 6.0;
        double r83242 = r83240 / r83241;
        return r83242;
}
↓
double f(double x) {
        double r83243 = x;
        double r83244 = r83243 * r83243;
        double r83245 = 6.0;
        double r83246 = r83244 / r83245;
        double r83247 = 3.0;
        double r83248 = r83247 / r83245;
        double r83249 = r83246 - r83248;
        return r83249;
}

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