Average Error: 0.2 → 0.2
Time: 16.1s
Precision: 64
\[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]
↓
\[y \cdot \left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right)\]
\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y
↓
y \cdot \left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right)
double f(double x, double y) {
        double r33249690 = x;
        double r33249691 = 16.0;
        double r33249692 = 116.0;
        double r33249693 = r33249691 / r33249692;
        double r33249694 = r33249690 - r33249693;
        double r33249695 = 3.0;
        double r33249696 = r33249694 * r33249695;
        double r33249697 = y;
        double r33249698 = r33249696 * r33249697;
        return r33249698;
}
↓
double f(double x, double y) {
        double r33249699 = y;
        double r33249700 = x;
        double r33249701 = 16.0;
        double r33249702 = 116.0;
        double r33249703 = r33249701 / r33249702;
        double r33249704 = r33249700 - r33249703;
        double r33249705 = 3.0;
        double r33249706 = r33249704 * r33249705;
        double r33249707 = r33249699 * r33249706;
        return r33249707;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.2
\[y \cdot \left(x \cdot 3.0 - 0.41379310344827586\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]

  2. Final simplification0.2

    \[\leadsto y \cdot \left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right)\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))