Average Error: 0.4 → 0.2
Time: 28.1s
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 r191478 = x;
        double r191479 = y;
        double r191480 = r191479 - r191478;
        double r191481 = 6.0;
        double r191482 = r191480 * r191481;
        double r191483 = 2.0;
        double r191484 = 3.0;
        double r191485 = r191483 / r191484;
        double r191486 = z;
        double r191487 = r191485 - r191486;
        double r191488 = r191482 * r191487;
        double r191489 = r191478 + r191488;
        return r191489;
}
↓
double f(double x, double y, double z) {
        double r191490 = x;
        double r191491 = y;
        double r191492 = r191491 - r191490;
        double r191493 = 2.0;
        double r191494 = 3.0;
        double r191495 = r191493 / r191494;
        double r191496 = z;
        double r191497 = r191495 - r191496;
        double r191498 = 6.0;
        double r191499 = r191497 * r191498;
        double r191500 = r191492 * r191499;
        double r191501 = r191490 + r191500;
        return r191501;
}

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))))