Average Error: 0.1 → 0.1
Time: 8.3s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x}{\frac{6}{x}} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x}{\frac{6}{x}} - \frac{3}{6}
double f(double x) {
        double r56419 = x;
        double r56420 = r56419 * r56419;
        double r56421 = 3.0;
        double r56422 = r56420 - r56421;
        double r56423 = 6.0;
        double r56424 = r56422 / r56423;
        return r56424;
}
↓
double f(double x) {
        double r56425 = x;
        double r56426 = 6.0;
        double r56427 = r56426 / r56425;
        double r56428 = r56425 / r56427;
        double r56429 = 3.0;
        double r56430 = r56429 / r56426;
        double r56431 = r56428 - r56430;
        return r56431;
}

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. Using strategy rm

  5. Applied associate-/l*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))