Average Error: 0.4 → 0.2
Time: 3.6s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(4 \cdot y - 3 \cdot x\right) + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(4 \cdot y - 3 \cdot x\right) + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)
double f(double x, double y, double z) {
        double r264674 = x;
        double r264675 = y;
        double r264676 = r264675 - r264674;
        double r264677 = 6.0;
        double r264678 = r264676 * r264677;
        double r264679 = 2.0;
        double r264680 = 3.0;
        double r264681 = r264679 / r264680;
        double r264682 = z;
        double r264683 = r264681 - r264682;
        double r264684 = r264678 * r264683;
        double r264685 = r264674 + r264684;
        return r264685;
}
↓
double f(double x, double y, double z) {
        double r264686 = 4.0;
        double r264687 = y;
        double r264688 = r264686 * r264687;
        double r264689 = 3.0;
        double r264690 = x;
        double r264691 = r264689 * r264690;
        double r264692 = r264688 - r264691;
        double r264693 = z;
        double r264694 = -r264693;
        double r264695 = r264687 - r264690;
        double r264696 = 6.0;
        double r264697 = r264695 * r264696;
        double r264698 = r264694 * r264697;
        double r264699 = r264692 + r264698;
        return r264699;
}

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 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-rgt-in0.4

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

  5. Applied associate-+r+0.4

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

  6. Taylor expanded around 0 0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020081 
(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))))