Average Error: 0.4 → 0.4
Time: 18.0s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r299908 = x;
        double r299909 = y;
        double r299910 = r299909 - r299908;
        double r299911 = 6.0;
        double r299912 = r299910 * r299911;
        double r299913 = 2.0;
        double r299914 = 3.0;
        double r299915 = r299913 / r299914;
        double r299916 = z;
        double r299917 = r299915 - r299916;
        double r299918 = r299912 * r299917;
        double r299919 = r299908 + r299918;
        return r299919;
}
↓
double f(double x, double y, double z) {
        double r299920 = x;
        double r299921 = y;
        double r299922 = r299921 - r299920;
        double r299923 = 6.0;
        double r299924 = r299922 * r299923;
        double r299925 = 2.0;
        double r299926 = 3.0;
        double r299927 = r299925 / r299926;
        double r299928 = r299924 * r299927;
        double r299929 = r299920 + r299928;
        double r299930 = z;
        double r299931 = -r299930;
        double r299932 = r299924 * r299931;
        double r299933 = r299929 + r299932;
        return r299933;
}

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. Applied associate-+r+0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019350 
(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))))