Average Error: 0.4 → 0.2
Time: 28.9s
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 r872998 = x;
        double r872999 = y;
        double r873000 = r872999 - r872998;
        double r873001 = 6.0;
        double r873002 = r873000 * r873001;
        double r873003 = 2.0;
        double r873004 = 3.0;
        double r873005 = r873003 / r873004;
        double r873006 = z;
        double r873007 = r873005 - r873006;
        double r873008 = r873002 * r873007;
        double r873009 = r872998 + r873008;
        return r873009;
}
↓
double f(double x, double y, double z) {
        double r873010 = x;
        double r873011 = y;
        double r873012 = r873011 - r873010;
        double r873013 = 2.0;
        double r873014 = 3.0;
        double r873015 = r873013 / r873014;
        double r873016 = z;
        double r873017 = r873015 - r873016;
        double r873018 = 6.0;
        double r873019 = r873017 * r873018;
        double r873020 = r873012 * r873019;
        double r873021 = r873010 + r873020;
        return r873021;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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*0.2

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

  4. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(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))))