Average Error: 0.4 → 0.2
Time: 5.6s
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 r334619 = x;
        double r334620 = y;
        double r334621 = r334620 - r334619;
        double r334622 = 6.0;
        double r334623 = r334621 * r334622;
        double r334624 = 2.0;
        double r334625 = 3.0;
        double r334626 = r334624 / r334625;
        double r334627 = z;
        double r334628 = r334626 - r334627;
        double r334629 = r334623 * r334628;
        double r334630 = r334619 + r334629;
        return r334630;
}
↓
double f(double x, double y, double z) {
        double r334631 = x;
        double r334632 = y;
        double r334633 = r334632 - r334631;
        double r334634 = 6.0;
        double r334635 = 2.0;
        double r334636 = 3.0;
        double r334637 = r334635 / r334636;
        double r334638 = z;
        double r334639 = r334637 - r334638;
        double r334640 = r334634 * r334639;
        double r334641 = r334633 * r334640;
        double r334642 = r334631 + r334641;
        return r334642;
}

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 2020021 
(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))))