Average Error: 0.4 → 0.2
Time: 8.9s
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 r359597 = x;
        double r359598 = y;
        double r359599 = r359598 - r359597;
        double r359600 = 6.0;
        double r359601 = r359599 * r359600;
        double r359602 = 2.0;
        double r359603 = 3.0;
        double r359604 = r359602 / r359603;
        double r359605 = z;
        double r359606 = r359604 - r359605;
        double r359607 = r359601 * r359606;
        double r359608 = r359597 + r359607;
        return r359608;
}
↓
double f(double x, double y, double z) {
        double r359609 = x;
        double r359610 = y;
        double r359611 = r359610 - r359609;
        double r359612 = 6.0;
        double r359613 = 2.0;
        double r359614 = 3.0;
        double r359615 = r359613 / r359614;
        double r359616 = z;
        double r359617 = r359615 - r359616;
        double r359618 = r359612 * r359617;
        double r359619 = r359611 * r359618;
        double r359620 = r359609 + r359619;
        return r359620;
}

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 2020027 
(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))))