Average Error: 0.1 → 0.1
Time: 2.0s
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 r49024 = x;
        double r49025 = r49024 * r49024;
        double r49026 = 3.0;
        double r49027 = r49025 - r49026;
        double r49028 = 6.0;
        double r49029 = r49027 / r49028;
        return r49029;
}
↓
double f(double x) {
        double r49030 = x;
        double r49031 = 6.0;
        double r49032 = r49031 / r49030;
        double r49033 = r49030 / r49032;
        double r49034 = 3.0;
        double r49035 = r49034 / r49031;
        double r49036 = r49033 - r49035;
        return r49036;
}

Error

Bits error versus x

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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 2019304 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))