Average Error: 0.1 → 0.2
Time: 9.1s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[0.1666666666666666574148081281236954964697 \cdot {x}^{2} - 0.5\]
\frac{x \cdot x - 3}{6}
↓
0.1666666666666666574148081281236954964697 \cdot {x}^{2} - 0.5
double f(double x) {
        double r42574 = x;
        double r42575 = r42574 * r42574;
        double r42576 = 3.0;
        double r42577 = r42575 - r42576;
        double r42578 = 6.0;
        double r42579 = r42577 / r42578;
        return r42579;
}
↓
double f(double x) {
        double r42580 = 0.16666666666666666;
        double r42581 = x;
        double r42582 = 2.0;
        double r42583 = pow(r42581, r42582);
        double r42584 = r42580 * r42583;
        double r42585 = 0.5;
        double r42586 = r42584 - r42585;
        return r42586;
}

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. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{0.1666666666666666574148081281236954964697 \cdot {x}^{2} - 0.5}\]

  3. Final simplification0.2

    \[\leadsto 0.1666666666666666574148081281236954964697 \cdot {x}^{2} - 0.5\]

Reproduce

herbie shell --seed 2019297 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))