Average Error: 0.4 → 0.2
Time: 7.5s
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 r287636 = x;
        double r287637 = y;
        double r287638 = r287637 - r287636;
        double r287639 = 6.0;
        double r287640 = r287638 * r287639;
        double r287641 = 2.0;
        double r287642 = 3.0;
        double r287643 = r287641 / r287642;
        double r287644 = z;
        double r287645 = r287643 - r287644;
        double r287646 = r287640 * r287645;
        double r287647 = r287636 + r287646;
        return r287647;
}
↓
double f(double x, double y, double z) {
        double r287648 = x;
        double r287649 = y;
        double r287650 = r287649 - r287648;
        double r287651 = 6.0;
        double r287652 = 2.0;
        double r287653 = 3.0;
        double r287654 = r287652 / r287653;
        double r287655 = z;
        double r287656 = r287654 - r287655;
        double r287657 = r287651 * r287656;
        double r287658 = r287650 * r287657;
        double r287659 = r287648 + r287658;
        return r287659;
}

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 2020056 
(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))))