Average Error: 0.4 → 0.2
Time: 26.0s
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 r205160 = x;
        double r205161 = y;
        double r205162 = r205161 - r205160;
        double r205163 = 6.0;
        double r205164 = r205162 * r205163;
        double r205165 = 2.0;
        double r205166 = 3.0;
        double r205167 = r205165 / r205166;
        double r205168 = z;
        double r205169 = r205167 - r205168;
        double r205170 = r205164 * r205169;
        double r205171 = r205160 + r205170;
        return r205171;
}
↓
double f(double x, double y, double z) {
        double r205172 = x;
        double r205173 = y;
        double r205174 = r205173 - r205172;
        double r205175 = 2.0;
        double r205176 = 3.0;
        double r205177 = r205175 / r205176;
        double r205178 = z;
        double r205179 = r205177 - r205178;
        double r205180 = 6.0;
        double r205181 = r205179 * r205180;
        double r205182 = r205174 * r205181;
        double r205183 = r205172 + r205182;
        return r205183;
}

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 2019322 
(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))))