Average Error: 0.4 → 0.2
Time: 13.4s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot 6\right)
double f(double x, double y, double z) {
        double r276016 = x;
        double r276017 = y;
        double r276018 = r276017 - r276016;
        double r276019 = 6.0;
        double r276020 = r276018 * r276019;
        double r276021 = 2.0;
        double r276022 = 3.0;
        double r276023 = r276021 / r276022;
        double r276024 = z;
        double r276025 = r276023 - r276024;
        double r276026 = r276020 * r276025;
        double r276027 = r276016 + r276026;
        return r276027;
}
↓
double f(double x, double y, double z) {
        double r276028 = x;
        double r276029 = y;
        double r276030 = r276029 - r276028;
        double r276031 = 2.0;
        double r276032 = 3.0;
        double r276033 = r276031 / r276032;
        double r276034 = z;
        double r276035 = r276033 - r276034;
        double r276036 = 6.0;
        double r276037 = r276035 * r276036;
        double r276038 = r276030 * r276037;
        double r276039 = r276028 + r276038;
        return r276039;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(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))))