Average Error: 0.4 → 0.4
Time: 51.3s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666296592325124947819858789 - z\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666296592325124947819858789 - z\right)
double f(double x, double y, double z) {
        double r14520779 = x;
        double r14520780 = y;
        double r14520781 = r14520780 - r14520779;
        double r14520782 = 6.0;
        double r14520783 = r14520781 * r14520782;
        double r14520784 = 2.0;
        double r14520785 = 3.0;
        double r14520786 = r14520784 / r14520785;
        double r14520787 = z;
        double r14520788 = r14520786 - r14520787;
        double r14520789 = r14520783 * r14520788;
        double r14520790 = r14520779 + r14520789;
        return r14520790;
}
↓
double f(double x, double y, double z) {
        double r14520791 = x;
        double r14520792 = y;
        double r14520793 = r14520792 - r14520791;
        double r14520794 = 6.0;
        double r14520795 = r14520793 * r14520794;
        double r14520796 = 0.6666666666666666;
        double r14520797 = z;
        double r14520798 = r14520796 - r14520797;
        double r14520799 = r14520795 * r14520798;
        double r14520800 = r14520791 + r14520799;
        return r14520800;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]

  2. Taylor expanded around 0 0.4

    \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(0.6666666666666666296592325124947819858789 - z\right)}\]

  3. Final simplification0.4

    \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666296592325124947819858789 - z\right)\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))