Average Error: 0.4 → 0.2
Time: 17.8s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(4 - 6 \cdot z\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(4 - 6 \cdot z\right)
double f(double x, double y, double z) {
        double r162060 = x;
        double r162061 = y;
        double r162062 = r162061 - r162060;
        double r162063 = 6.0;
        double r162064 = r162062 * r162063;
        double r162065 = 2.0;
        double r162066 = 3.0;
        double r162067 = r162065 / r162066;
        double r162068 = z;
        double r162069 = r162067 - r162068;
        double r162070 = r162064 * r162069;
        double r162071 = r162060 + r162070;
        return r162071;
}
↓
double f(double x, double y, double z) {
        double r162072 = x;
        double r162073 = y;
        double r162074 = r162073 - r162072;
        double r162075 = 4.0;
        double r162076 = 6.0;
        double r162077 = z;
        double r162078 = r162076 * r162077;
        double r162079 = r162075 - r162078;
        double r162080 = r162074 * r162079;
        double r162081 = r162072 + r162080;
        return r162081;
}

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. Simplified0.2

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

  5. Taylor expanded around 0 0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))