Average Error: 0.1 → 0.2
Time: 2.6s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{1}{6 \cdot \frac{1}{x \cdot x - 3}}\]
\frac{x \cdot x - 3}{6}
↓
\frac{1}{6 \cdot \frac{1}{x \cdot x - 3}}
double f(double x) {
        double r77422 = x;
        double r77423 = r77422 * r77422;
        double r77424 = 3.0;
        double r77425 = r77423 - r77424;
        double r77426 = 6.0;
        double r77427 = r77425 / r77426;
        return r77427;
}
↓
double f(double x) {
        double r77428 = 1.0;
        double r77429 = 6.0;
        double r77430 = x;
        double r77431 = r77430 * r77430;
        double r77432 = 3.0;
        double r77433 = r77431 - r77432;
        double r77434 = r77428 / r77433;
        double r77435 = r77429 * r77434;
        double r77436 = r77428 / r77435;
        return r77436;
}

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 clear-num0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{6}{x \cdot x - 3}}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

    \[\leadsto \frac{1}{\color{blue}{6 \cdot \frac{1}{x \cdot x - 3}}}\]

  6. Final simplification0.2

    \[\leadsto \frac{1}{6 \cdot \frac{1}{x \cdot x - 3}}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))