Average Error: 0.4 → 0.2
Time: 3.0s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right) + \left(y - x\right) \cdot \left(\left(-z\right) \cdot 6\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right) + \left(y - x\right) \cdot \left(\left(-z\right) \cdot 6\right)\right)
double f(double x, double y, double z) {
        double r251991 = x;
        double r251992 = y;
        double r251993 = r251992 - r251991;
        double r251994 = 6.0;
        double r251995 = r251993 * r251994;
        double r251996 = 2.0;
        double r251997 = 3.0;
        double r251998 = r251996 / r251997;
        double r251999 = z;
        double r252000 = r251998 - r251999;
        double r252001 = r251995 * r252000;
        double r252002 = r251991 + r252001;
        return r252002;
}
↓
double f(double x, double y, double z) {
        double r252003 = x;
        double r252004 = y;
        double r252005 = r252004 - r252003;
        double r252006 = 2.0;
        double r252007 = 3.0;
        double r252008 = r252006 / r252007;
        double r252009 = 6.0;
        double r252010 = r252008 * r252009;
        double r252011 = r252005 * r252010;
        double r252012 = z;
        double r252013 = -r252012;
        double r252014 = r252013 * r252009;
        double r252015 = r252005 * r252014;
        double r252016 = r252011 + r252015;
        double r252017 = r252003 + r252016;
        return r252017;
}

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. Using strategy rm

  5. Applied sub-neg0.2

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

  6. Applied distribute-lft-in0.2

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

  7. Applied distribute-lft-in0.2

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

  8. Simplified0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(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))))