Average Error: 0.1 → 0.2
Time: 2.5s
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 r94126 = x;
        double r94127 = r94126 * r94126;
        double r94128 = 3.0;
        double r94129 = r94127 - r94128;
        double r94130 = 6.0;
        double r94131 = r94129 / r94130;
        return r94131;
}
↓
double f(double x) {
        double r94132 = 1.0;
        double r94133 = 6.0;
        double r94134 = x;
        double r94135 = r94134 * r94134;
        double r94136 = 3.0;
        double r94137 = r94135 - r94136;
        double r94138 = r94132 / r94137;
        double r94139 = r94133 * r94138;
        double r94140 = r94132 / r94139;
        return r94140;
}

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