Average Error: 0.4 → 0.2
Time: 21.8s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)\]
x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)
↓
x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)
double f(double x, double y, double z) {
        double r13444248 = x;
        double r13444249 = y;
        double r13444250 = r13444249 - r13444248;
        double r13444251 = 6.0;
        double r13444252 = r13444250 * r13444251;
        double r13444253 = 2.0;
        double r13444254 = 3.0;
        double r13444255 = r13444253 / r13444254;
        double r13444256 = z;
        double r13444257 = r13444255 - r13444256;
        double r13444258 = r13444252 * r13444257;
        double r13444259 = r13444248 + r13444258;
        return r13444259;
}
↓
double f(double x, double y, double z) {
        double r13444260 = x;
        double r13444261 = y;
        double r13444262 = r13444261 - r13444260;
        double r13444263 = 2.0;
        double r13444264 = 3.0;
        double r13444265 = r13444263 / r13444264;
        double r13444266 = z;
        double r13444267 = r13444265 - r13444266;
        double r13444268 = 6.0;
        double r13444269 = r13444267 * r13444268;
        double r13444270 = r13444262 * r13444269;
        double r13444271 = r13444260 + r13444270;
        return r13444271;
}

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

    \[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6.0 \cdot \left(\frac{2.0}{3.0} - z\right)\right)}\]

  4. Final simplification0.2

    \[\leadsto x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)\]

Reproduce

herbie shell --seed 2019163 
(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))))