Average Error: 0.4 → 0.2
Time: 26.1s
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 r191665 = x;
        double r191666 = y;
        double r191667 = r191666 - r191665;
        double r191668 = 6.0;
        double r191669 = r191667 * r191668;
        double r191670 = 2.0;
        double r191671 = 3.0;
        double r191672 = r191670 / r191671;
        double r191673 = z;
        double r191674 = r191672 - r191673;
        double r191675 = r191669 * r191674;
        double r191676 = r191665 + r191675;
        return r191676;
}
↓
double f(double x, double y, double z) {
        double r191677 = x;
        double r191678 = y;
        double r191679 = r191678 - r191677;
        double r191680 = 2.0;
        double r191681 = 3.0;
        double r191682 = r191680 / r191681;
        double r191683 = z;
        double r191684 = r191682 - r191683;
        double r191685 = 6.0;
        double r191686 = r191684 * r191685;
        double r191687 = r191679 * r191686;
        double r191688 = r191677 + r191687;
        return r191688;
}

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))))