Average Error: 0.4 → 0.2
Time: 21.4s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)\]
x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)
↓
x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)
double f(double x, double y, double z) {
        double r11943787 = x;
        double r11943788 = y;
        double r11943789 = r11943788 - r11943787;
        double r11943790 = 6.0;
        double r11943791 = r11943789 * r11943790;
        double r11943792 = 2.0;
        double r11943793 = 3.0;
        double r11943794 = r11943792 / r11943793;
        double r11943795 = z;
        double r11943796 = r11943794 - r11943795;
        double r11943797 = r11943791 * r11943796;
        double r11943798 = r11943787 + r11943797;
        return r11943798;
}
↓
double f(double x, double y, double z) {
        double r11943799 = x;
        double r11943800 = y;
        double r11943801 = r11943800 - r11943799;
        double r11943802 = 2.0;
        double r11943803 = 3.0;
        double r11943804 = r11943802 / r11943803;
        double r11943805 = z;
        double r11943806 = r11943804 - r11943805;
        double r11943807 = 6.0;
        double r11943808 = r11943806 * r11943807;
        double r11943809 = r11943801 * r11943808;
        double r11943810 = r11943799 + r11943809;
        return r11943810;
}

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

    \[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6.0 \cdot \left(\frac{2.0}{3.0} - z\right)\right)}\]

  4. Final simplification0.2

    \[\leadsto x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)\]

Reproduce

herbie shell --seed 2019162 +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))))