Average Error: 0.4 → 0.2
Time: 3.5s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[4 \cdot y + \left(6 \cdot \left(x \cdot z - z \cdot y\right) - 3 \cdot x\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
4 \cdot y + \left(6 \cdot \left(x \cdot z - z \cdot y\right) - 3 \cdot x\right)
double f(double x, double y, double z) {
        double r264770 = x;
        double r264771 = y;
        double r264772 = r264771 - r264770;
        double r264773 = 6.0;
        double r264774 = r264772 * r264773;
        double r264775 = 2.0;
        double r264776 = 3.0;
        double r264777 = r264775 / r264776;
        double r264778 = z;
        double r264779 = r264777 - r264778;
        double r264780 = r264774 * r264779;
        double r264781 = r264770 + r264780;
        return r264781;
}
↓
double f(double x, double y, double z) {
        double r264782 = 4.0;
        double r264783 = y;
        double r264784 = r264782 * r264783;
        double r264785 = 6.0;
        double r264786 = x;
        double r264787 = z;
        double r264788 = r264786 * r264787;
        double r264789 = r264787 * r264783;
        double r264790 = r264788 - r264789;
        double r264791 = r264785 * r264790;
        double r264792 = 3.0;
        double r264793 = r264792 * r264786;
        double r264794 = r264791 - r264793;
        double r264795 = r264784 + r264794;
        return r264795;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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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 sub-neg0.4

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

  4. Applied distribute-lft-in0.4

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

  5. Applied associate-+r+0.4

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

  6. Simplified0.4

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

  7. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(4 \cdot y - 3 \cdot x\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\]
  8. Using strategy rm

  9. Applied sub-neg0.2

    \[\leadsto \color{blue}{\left(4 \cdot y + \left(-3 \cdot x\right)\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\]

  10. Applied associate-+l+0.2

    \[\leadsto \color{blue}{4 \cdot y + \left(\left(-3 \cdot x\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\right)}\]

  11. Simplified0.2

    \[\leadsto 4 \cdot y + \color{blue}{\left(6 \cdot \left(x \cdot z - z \cdot y\right) - 3 \cdot x\right)}\]

  12. Final simplification0.2

    \[\leadsto 4 \cdot y + \left(6 \cdot \left(x \cdot z - z \cdot y\right) - 3 \cdot x\right)\]

Reproduce

herbie shell --seed 2020100 
(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))))