Average Error: 0.4 → 0.2
Time: 11.5s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + \left(z \cdot \left(x - y\right)\right) \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + \left(z \cdot \left(x - y\right)\right) \cdot 6\right)
double f(double x, double y, double z) {
        double r291739 = x;
        double r291740 = y;
        double r291741 = r291740 - r291739;
        double r291742 = 6.0;
        double r291743 = r291741 * r291742;
        double r291744 = 2.0;
        double r291745 = 3.0;
        double r291746 = r291744 / r291745;
        double r291747 = z;
        double r291748 = r291746 - r291747;
        double r291749 = r291743 * r291748;
        double r291750 = r291739 + r291749;
        return r291750;
}
↓
double f(double x, double y, double z) {
        double r291751 = x;
        double r291752 = y;
        double r291753 = r291752 - r291751;
        double r291754 = 6.0;
        double r291755 = 2.0;
        double r291756 = 3.0;
        double r291757 = r291755 / r291756;
        double r291758 = r291754 * r291757;
        double r291759 = r291753 * r291758;
        double r291760 = z;
        double r291761 = r291751 - r291752;
        double r291762 = r291760 * r291761;
        double r291763 = r291762 * r291754;
        double r291764 = r291759 + r291763;
        double r291765 = r291751 + r291764;
        return r291765;
}

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. Using strategy rm

  5. Applied sub-neg0.2

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

  6. Applied distribute-lft-in0.2

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

  7. Applied distribute-lft-in0.2

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

  8. Taylor expanded around inf 0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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))))