Average Error: 0.2 → 0.2
Time: 15.3s
Precision: 64
\[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]
↓
\[\left(x \cdot 3.0 - 0.41379310344827586\right) \cdot y\]
\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y
↓
\left(x \cdot 3.0 - 0.41379310344827586\right) \cdot y
double f(double x, double y) {
        double r35694688 = x;
        double r35694689 = 16.0;
        double r35694690 = 116.0;
        double r35694691 = r35694689 / r35694690;
        double r35694692 = r35694688 - r35694691;
        double r35694693 = 3.0;
        double r35694694 = r35694692 * r35694693;
        double r35694695 = y;
        double r35694696 = r35694694 * r35694695;
        return r35694696;
}
↓
double f(double x, double y) {
        double r35694697 = x;
        double r35694698 = 3.0;
        double r35694699 = r35694697 * r35694698;
        double r35694700 = 0.41379310344827586;
        double r35694701 = r35694699 - r35694700;
        double r35694702 = y;
        double r35694703 = r35694701 * r35694702;
        return r35694703;
}

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. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{3.0 \cdot \left(x \cdot y\right) - 0.41379310344827586 \cdot y}\]

  3. Simplified0.2

    \[\leadsto \color{blue}{y \cdot \left(3.0 \cdot x - 0.41379310344827586\right)}\]

  4. Final simplification0.2

    \[\leadsto \left(x \cdot 3.0 - 0.41379310344827586\right) \cdot y\]

Reproduce

herbie shell --seed 2019163 +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))