Average Error: 0.4 → 0.2
Time: 24.7s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(x + \left(y - x\right) \cdot \frac{6}{\frac{3}{2}}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(x + \left(y - x\right) \cdot \frac{6}{\frac{3}{2}}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r138950 = x;
        double r138951 = y;
        double r138952 = r138951 - r138950;
        double r138953 = 6.0;
        double r138954 = r138952 * r138953;
        double r138955 = 2.0;
        double r138956 = 3.0;
        double r138957 = r138955 / r138956;
        double r138958 = z;
        double r138959 = r138957 - r138958;
        double r138960 = r138954 * r138959;
        double r138961 = r138950 + r138960;
        return r138961;
}
↓
double f(double x, double y, double z) {
        double r138962 = x;
        double r138963 = y;
        double r138964 = r138963 - r138962;
        double r138965 = 6.0;
        double r138966 = 3.0;
        double r138967 = 2.0;
        double r138968 = r138966 / r138967;
        double r138969 = r138965 / r138968;
        double r138970 = r138964 * r138969;
        double r138971 = r138962 + r138970;
        double r138972 = r138964 * r138965;
        double r138973 = z;
        double r138974 = -r138973;
        double r138975 = r138972 * r138974;
        double r138976 = r138971 + r138975;
        return r138976;
}

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 sub-neg0.4

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

  4. Applied distribute-lft-in0.4

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

  5. Applied associate-+r+0.4

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

  7. Applied associate-*l*0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019326 
(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))))