Average Error: 0.4 → 0.2
Time: 3.5s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + \left(z \cdot \left(x - y\right)\right) \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + \left(z \cdot \left(x - y\right)\right) \cdot 6\right)
double f(double x, double y, double z) {
        double r218843 = x;
        double r218844 = y;
        double r218845 = r218844 - r218843;
        double r218846 = 6.0;
        double r218847 = r218845 * r218846;
        double r218848 = 2.0;
        double r218849 = 3.0;
        double r218850 = r218848 / r218849;
        double r218851 = z;
        double r218852 = r218850 - r218851;
        double r218853 = r218847 * r218852;
        double r218854 = r218843 + r218853;
        return r218854;
}
↓
double f(double x, double y, double z) {
        double r218855 = x;
        double r218856 = y;
        double r218857 = r218856 - r218855;
        double r218858 = 6.0;
        double r218859 = 2.0;
        double r218860 = 3.0;
        double r218861 = r218859 / r218860;
        double r218862 = r218858 * r218861;
        double r218863 = r218857 * r218862;
        double r218864 = z;
        double r218865 = r218855 - r218856;
        double r218866 = r218864 * r218865;
        double r218867 = r218866 * r218858;
        double r218868 = r218863 + r218867;
        double r218869 = r218855 + r218868;
        return r218869;
}

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-lft-in0.4

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

  6. Applied associate-*l*0.2

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

  7. Taylor expanded around inf 0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020024 
(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))))