Average Error: 0.4 → 0.2
Time: 10.7s
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 r244238 = x;
        double r244239 = y;
        double r244240 = r244239 - r244238;
        double r244241 = 6.0;
        double r244242 = r244240 * r244241;
        double r244243 = 2.0;
        double r244244 = 3.0;
        double r244245 = r244243 / r244244;
        double r244246 = z;
        double r244247 = r244245 - r244246;
        double r244248 = r244242 * r244247;
        double r244249 = r244238 + r244248;
        return r244249;
}
↓
double f(double x, double y, double z) {
        double r244250 = x;
        double r244251 = y;
        double r244252 = r244251 - r244250;
        double r244253 = 2.0;
        double r244254 = 3.0;
        double r244255 = r244253 / r244254;
        double r244256 = z;
        double r244257 = r244255 - r244256;
        double r244258 = 6.0;
        double r244259 = r244257 * r244258;
        double r244260 = r244252 * r244259;
        double r244261 = r244250 + r244260;
        return r244261;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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 2019235 
(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))))