Average Error: 0.1 → 0.2
Time: 2.4s
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 r84128 = x;
        double r84129 = r84128 * r84128;
        double r84130 = 3.0;
        double r84131 = r84129 - r84130;
        double r84132 = 6.0;
        double r84133 = r84131 / r84132;
        return r84133;
}
↓
double f(double x) {
        double r84134 = 1.0;
        double r84135 = 6.0;
        double r84136 = x;
        double r84137 = r84136 * r84136;
        double r84138 = 3.0;
        double r84139 = r84137 - r84138;
        double r84140 = r84135 / r84139;
        double r84141 = r84134 / r84140;
        return r84141;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))