Average Error: 0.4 → 0.2
Time: 27.5s
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 r231366 = x;
        double r231367 = y;
        double r231368 = r231367 - r231366;
        double r231369 = 6.0;
        double r231370 = r231368 * r231369;
        double r231371 = 2.0;
        double r231372 = 3.0;
        double r231373 = r231371 / r231372;
        double r231374 = z;
        double r231375 = r231373 - r231374;
        double r231376 = r231370 * r231375;
        double r231377 = r231366 + r231376;
        return r231377;
}
↓
double f(double x, double y, double z) {
        double r231378 = x;
        double r231379 = y;
        double r231380 = r231379 - r231378;
        double r231381 = 2.0;
        double r231382 = 3.0;
        double r231383 = r231381 / r231382;
        double r231384 = z;
        double r231385 = r231383 - r231384;
        double r231386 = 6.0;
        double r231387 = r231385 * r231386;
        double r231388 = r231380 * r231387;
        double r231389 = r231378 + r231388;
        return r231389;
}

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 2019323 
(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))))