Average Error: 0.4 → 0.2
Time: 14.3s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(4 - 6 \cdot z\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(4 - 6 \cdot z\right)
double f(double x, double y, double z) {
        double r234657 = x;
        double r234658 = y;
        double r234659 = r234658 - r234657;
        double r234660 = 6.0;
        double r234661 = r234659 * r234660;
        double r234662 = 2.0;
        double r234663 = 3.0;
        double r234664 = r234662 / r234663;
        double r234665 = z;
        double r234666 = r234664 - r234665;
        double r234667 = r234661 * r234666;
        double r234668 = r234657 + r234667;
        return r234668;
}
↓
double f(double x, double y, double z) {
        double r234669 = x;
        double r234670 = y;
        double r234671 = r234670 - r234669;
        double r234672 = 4.0;
        double r234673 = 6.0;
        double r234674 = z;
        double r234675 = r234673 * r234674;
        double r234676 = r234672 - r234675;
        double r234677 = r234671 * r234676;
        double r234678 = r234669 + r234677;
        return r234678;
}

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. Taylor expanded around 0 0.2

    \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(4 - 6 \cdot z\right)}\]

  6. Final simplification0.2

    \[\leadsto x + \left(y - x\right) \cdot \left(4 - 6 \cdot z\right)\]

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))