Average Error: 0.4 → 0.3
Time: 15.0s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot 6\right)
double f(double x, double y, double z) {
        double r381788 = x;
        double r381789 = y;
        double r381790 = r381789 - r381788;
        double r381791 = 6.0;
        double r381792 = r381790 * r381791;
        double r381793 = 2.0;
        double r381794 = 3.0;
        double r381795 = r381793 / r381794;
        double r381796 = z;
        double r381797 = r381795 - r381796;
        double r381798 = r381792 * r381797;
        double r381799 = r381788 + r381798;
        return r381799;
}
↓
double f(double x, double y, double z) {
        double r381800 = x;
        double r381801 = y;
        double r381802 = r381801 - r381800;
        double r381803 = 2.0;
        double r381804 = 3.0;
        double r381805 = r381803 / r381804;
        double r381806 = z;
        double r381807 = r381805 - r381806;
        double r381808 = 6.0;
        double r381809 = r381807 * r381808;
        double r381810 = r381802 * r381809;
        double r381811 = r381800 + r381810;
        return r381811;
}

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. Simplified0.3

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

  5. Final simplification0.3

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

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))))