Average Error: 0.4 → 0.2
Time: 3.5s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)
double f(double x, double y, double z) {
        double r241668 = x;
        double r241669 = y;
        double r241670 = r241669 - r241668;
        double r241671 = 6.0;
        double r241672 = r241670 * r241671;
        double r241673 = 2.0;
        double r241674 = 3.0;
        double r241675 = r241673 / r241674;
        double r241676 = z;
        double r241677 = r241675 - r241676;
        double r241678 = r241672 * r241677;
        double r241679 = r241668 + r241678;
        return r241679;
}
↓
double f(double x, double y, double z) {
        double r241680 = x;
        double r241681 = y;
        double r241682 = r241681 - r241680;
        double r241683 = 6.0;
        double r241684 = 2.0;
        double r241685 = 3.0;
        double r241686 = r241684 / r241685;
        double r241687 = z;
        double r241688 = r241686 - r241687;
        double r241689 = r241683 * r241688;
        double r241690 = r241682 * r241689;
        double r241691 = r241680 + r241690;
        return r241691;
}

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

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

Reproduce

herbie shell --seed 2019362 
(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))))