Average Error: 0.4 → 0.3
Time: 12.6s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)
double f(double x, double y, double z) {
        double r328877 = x;
        double r328878 = y;
        double r328879 = r328878 - r328877;
        double r328880 = 6.0;
        double r328881 = r328879 * r328880;
        double r328882 = 2.0;
        double r328883 = 3.0;
        double r328884 = r328882 / r328883;
        double r328885 = z;
        double r328886 = r328884 - r328885;
        double r328887 = r328881 * r328886;
        double r328888 = r328877 + r328887;
        return r328888;
}
↓
double f(double x, double y, double z) {
        double r328889 = x;
        double r328890 = y;
        double r328891 = r328890 - r328889;
        double r328892 = 6.0;
        double r328893 = 2.0;
        double r328894 = 3.0;
        double r328895 = r328893 / r328894;
        double r328896 = z;
        double r328897 = r328895 - r328896;
        double r328898 = r328892 * r328897;
        double r328899 = r328891 * r328898;
        double r328900 = r328889 + r328899;
        return r328900;
}

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 associate-*l*0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 
(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))))