Average Error: 0.1 → 0.1
Time: 1.8s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\left(x \cdot 0.166666666666666657\right) \cdot {x}^{1} - 0.5\]
\frac{x \cdot x - 3}{6}
↓
\left(x \cdot 0.166666666666666657\right) \cdot {x}^{1} - 0.5
double f(double x) {
        double r82092 = x;
        double r82093 = r82092 * r82092;
        double r82094 = 3.0;
        double r82095 = r82093 - r82094;
        double r82096 = 6.0;
        double r82097 = r82095 / r82096;
        return r82097;
}
↓
double f(double x) {
        double r82098 = x;
        double r82099 = 0.16666666666666666;
        double r82100 = r82098 * r82099;
        double r82101 = 1.0;
        double r82102 = pow(r82098, r82101);
        double r82103 = r82100 * r82102;
        double r82104 = 0.5;
        double r82105 = r82103 - r82104;
        return r82105;
}

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. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{0.166666666666666657 \cdot {x}^{2} - 0.5}\]
  3. Using strategy rm

  4. Applied sqr-pow0.2

    \[\leadsto 0.166666666666666657 \cdot \color{blue}{\left({x}^{\left(\frac{2}{2}\right)} \cdot {x}^{\left(\frac{2}{2}\right)}\right)} - 0.5\]

  5. Applied associate-*r*0.1

    \[\leadsto \color{blue}{\left(0.166666666666666657 \cdot {x}^{\left(\frac{2}{2}\right)}\right) \cdot {x}^{\left(\frac{2}{2}\right)}} - 0.5\]

  6. Simplified0.1

    \[\leadsto \color{blue}{\left(x \cdot 0.166666666666666657\right)} \cdot {x}^{\left(\frac{2}{2}\right)} - 0.5\]

  7. Final simplification0.1

    \[\leadsto \left(x \cdot 0.166666666666666657\right) \cdot {x}^{1} - 0.5\]

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))