Average Error: 0.4 → 0.2
Time: 15.4s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(4 \cdot y - 3 \cdot x\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(4 \cdot y - 3 \cdot x\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r309901 = x;
        double r309902 = y;
        double r309903 = r309902 - r309901;
        double r309904 = 6.0;
        double r309905 = r309903 * r309904;
        double r309906 = 2.0;
        double r309907 = 3.0;
        double r309908 = r309906 / r309907;
        double r309909 = z;
        double r309910 = r309908 - r309909;
        double r309911 = r309905 * r309910;
        double r309912 = r309901 + r309911;
        return r309912;
}
↓
double f(double x, double y, double z) {
        double r309913 = 4.0;
        double r309914 = y;
        double r309915 = r309913 * r309914;
        double r309916 = 3.0;
        double r309917 = x;
        double r309918 = r309916 * r309917;
        double r309919 = r309915 - r309918;
        double r309920 = r309914 - r309917;
        double r309921 = 6.0;
        double r309922 = r309920 * r309921;
        double r309923 = z;
        double r309924 = -r309923;
        double r309925 = r309922 * r309924;
        double r309926 = r309919 + r309925;
        return r309926;
}

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. Simplified0.4

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

  7. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(4 \cdot y - 3 \cdot x\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\]

  8. Final simplification0.2

    \[\leadsto \left(4 \cdot y - 3 \cdot x\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(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))))