Average Error: 0.4 → 0.2
Time: 14.4s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(\left(\frac{2}{3} \cdot 6\right) \cdot y + \left(6 \cdot \left(\left(x - y\right) \cdot z\right) - \left(\frac{2}{3} \cdot 6\right) \cdot x\right)\right) + x\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(\left(\frac{2}{3} \cdot 6\right) \cdot y + \left(6 \cdot \left(\left(x - y\right) \cdot z\right) - \left(\frac{2}{3} \cdot 6\right) \cdot x\right)\right) + x
double f(double x, double y, double z) {
        double r189797 = x;
        double r189798 = y;
        double r189799 = r189798 - r189797;
        double r189800 = 6.0;
        double r189801 = r189799 * r189800;
        double r189802 = 2.0;
        double r189803 = 3.0;
        double r189804 = r189802 / r189803;
        double r189805 = z;
        double r189806 = r189804 - r189805;
        double r189807 = r189801 * r189806;
        double r189808 = r189797 + r189807;
        return r189808;
}
↓
double f(double x, double y, double z) {
        double r189809 = 2.0;
        double r189810 = 3.0;
        double r189811 = r189809 / r189810;
        double r189812 = 6.0;
        double r189813 = r189811 * r189812;
        double r189814 = y;
        double r189815 = r189813 * r189814;
        double r189816 = x;
        double r189817 = r189816 - r189814;
        double r189818 = z;
        double r189819 = r189817 * r189818;
        double r189820 = r189812 * r189819;
        double r189821 = r189813 * r189816;
        double r189822 = r189820 - r189821;
        double r189823 = r189815 + r189822;
        double r189824 = r189823 + r189816;
        return r189824;
}

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. Simplified0.4

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

  4. Applied sub-neg0.4

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

  5. Applied distribute-lft-in0.4

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

  6. Applied distribute-lft-in0.4

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

  7. Simplified0.2

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

  8. Simplified0.2

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

  10. Applied sub-neg0.2

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

  11. Applied distribute-lft-in0.2

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

  12. Applied associate-+l+0.2

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019196 
(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))))