Average Error: 0.4 → 0.2
Time: 3.6s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(4 \cdot y - 3 \cdot x\right) + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(4 \cdot y - 3 \cdot x\right) + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)
double f(double x, double y, double z) {
        double r314785 = x;
        double r314786 = y;
        double r314787 = r314786 - r314785;
        double r314788 = 6.0;
        double r314789 = r314787 * r314788;
        double r314790 = 2.0;
        double r314791 = 3.0;
        double r314792 = r314790 / r314791;
        double r314793 = z;
        double r314794 = r314792 - r314793;
        double r314795 = r314789 * r314794;
        double r314796 = r314785 + r314795;
        return r314796;
}
↓
double f(double x, double y, double z) {
        double r314797 = 4.0;
        double r314798 = y;
        double r314799 = r314797 * r314798;
        double r314800 = 3.0;
        double r314801 = x;
        double r314802 = r314800 * r314801;
        double r314803 = r314799 - r314802;
        double r314804 = z;
        double r314805 = -r314804;
        double r314806 = r314798 - r314801;
        double r314807 = 6.0;
        double r314808 = r314806 * r314807;
        double r314809 = r314805 * r314808;
        double r314810 = r314803 + r314809;
        return r314810;
}

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. Using strategy rm

  3. Applied sub-neg0.4

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

  4. Applied distribute-rgt-in0.4

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

  5. Applied associate-+r+0.4

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

  6. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(4 \cdot y - 3 \cdot x\right)} + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)\]

  7. Final simplification0.2

    \[\leadsto \left(4 \cdot y - 3 \cdot x\right) + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)\]

Reproduce

herbie shell --seed 2020035 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6) (- (/ 2 3) z))))