Average Error: 0.2 → 0.2
Time: 3.2s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{1}{\frac{6}{x \cdot x - 3}}\]
\frac{x \cdot x - 3}{6}
↓
\frac{1}{\frac{6}{x \cdot x - 3}}
double f(double x) {
        double r409 = x;
        double r410 = r409 * r409;
        double r411 = 3.0;
        double r412 = r410 - r411;
        double r413 = 6.0;
        double r414 = r412 / r413;
        return r414;
}
↓
double f(double x) {
        double r415 = 1.0;
        double r416 = 6.0;
        double r417 = x;
        double r418 = r417 * r417;
        double r419 = 3.0;
        double r420 = r418 - r419;
        double r421 = r416 / r420;
        double r422 = r415 / r421;
        return r422;
}

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 clear-num0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))