Average Error: 0.1 → 0.2
Time: 2.3s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[0.166666666666666657 \cdot {x}^{2} - 0.5\]
\frac{x \cdot x - 3}{6}
↓
0.166666666666666657 \cdot {x}^{2} - 0.5
double f(double x) {
        double r76668 = x;
        double r76669 = r76668 * r76668;
        double r76670 = 3.0;
        double r76671 = r76669 - r76670;
        double r76672 = 6.0;
        double r76673 = r76671 / r76672;
        return r76673;
}
↓
double f(double x) {
        double r76674 = 0.16666666666666666;
        double r76675 = x;
        double r76676 = 2.0;
        double r76677 = pow(r76675, r76676);
        double r76678 = r76674 * r76677;
        double r76679 = 0.5;
        double r76680 = r76678 - r76679;
        return r76680;
}

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

    \[\leadsto \color{blue}{0.166666666666666657 \cdot {x}^{2} - 0.5}\]

  3. Final simplification0.2

    \[\leadsto 0.166666666666666657 \cdot {x}^{2} - 0.5\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))