Average Error: 0.4 → 0.2
Time: 19.9s
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 r11230040 = x;
        double r11230041 = y;
        double r11230042 = r11230041 - r11230040;
        double r11230043 = 6.0;
        double r11230044 = r11230042 * r11230043;
        double r11230045 = 2.0;
        double r11230046 = 3.0;
        double r11230047 = r11230045 / r11230046;
        double r11230048 = z;
        double r11230049 = r11230047 - r11230048;
        double r11230050 = r11230044 * r11230049;
        double r11230051 = r11230040 + r11230050;
        return r11230051;
}
↓
double f(double x, double y, double z) {
        double r11230052 = x;
        double r11230053 = y;
        double r11230054 = r11230053 - r11230052;
        double r11230055 = 2.0;
        double r11230056 = 3.0;
        double r11230057 = r11230055 / r11230056;
        double r11230058 = z;
        double r11230059 = r11230057 - r11230058;
        double r11230060 = 6.0;
        double r11230061 = r11230059 * r11230060;
        double r11230062 = r11230054 * r11230061;
        double r11230063 = r11230052 + r11230062;
        return r11230063;
}

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*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))