Average Error: 0.4 → 0.2
Time: 3.6s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)
double f(double x, double y, double z) {
        double r296381 = x;
        double r296382 = y;
        double r296383 = r296382 - r296381;
        double r296384 = 6.0;
        double r296385 = r296383 * r296384;
        double r296386 = 2.0;
        double r296387 = 3.0;
        double r296388 = r296386 / r296387;
        double r296389 = z;
        double r296390 = r296388 - r296389;
        double r296391 = r296385 * r296390;
        double r296392 = r296381 + r296391;
        return r296392;
}
↓
double f(double x, double y, double z) {
        double r296393 = x;
        double r296394 = y;
        double r296395 = r296394 - r296393;
        double r296396 = 6.0;
        double r296397 = 2.0;
        double r296398 = 3.0;
        double r296399 = r296397 / r296398;
        double r296400 = z;
        double r296401 = r296399 - r296400;
        double r296402 = r296396 * r296401;
        double r296403 = r296395 * r296402;
        double r296404 = r296393 + r296403;
        return r296404;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020057 
(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))))