Average Error: 0.4 → 0.2
Time: 14.6s
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 r358626 = x;
        double r358627 = y;
        double r358628 = r358627 - r358626;
        double r358629 = 6.0;
        double r358630 = r358628 * r358629;
        double r358631 = 2.0;
        double r358632 = 3.0;
        double r358633 = r358631 / r358632;
        double r358634 = z;
        double r358635 = r358633 - r358634;
        double r358636 = r358630 * r358635;
        double r358637 = r358626 + r358636;
        return r358637;
}
↓
double f(double x, double y, double z) {
        double r358638 = x;
        double r358639 = y;
        double r358640 = r358639 - r358638;
        double r358641 = 6.0;
        double r358642 = 2.0;
        double r358643 = 3.0;
        double r358644 = r358642 / r358643;
        double r358645 = z;
        double r358646 = r358644 - r358645;
        double r358647 = r358641 * r358646;
        double r358648 = r358640 * r358647;
        double r358649 = r358638 + r358648;
        return r358649;
}

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 2019303 
(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))))