Average Error: 0.2 → 0.1
Time: 18.0s
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 r55944 = x;
        double r55945 = r55944 * r55944;
        double r55946 = 3.0;
        double r55947 = r55945 - r55946;
        double r55948 = 6.0;
        double r55949 = r55947 / r55948;
        return r55949;
}
↓
double f(double x) {
        double r55950 = x;
        double r55951 = 6.0;
        double r55952 = r55951 / r55950;
        double r55953 = r55950 / r55952;
        double r55954 = 3.0;
        double r55955 = r55954 / r55951;
        double r55956 = r55953 - r55955;
        return r55956;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{x \cdot x - 3}{6}\]
  2. Using strategy rm

  3. Applied div-sub0.1

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

  4. Simplified0.1

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

  6. Applied associate-*l/0.1

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

  8. Applied associate-/l*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))