Average Error: 0.2 → 0.3
Time: 16.9s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(3 \cdot y\right) \cdot \left(x - \frac{16}{116}\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(3 \cdot y\right) \cdot \left(x - \frac{16}{116}\right)
double f(double x, double y) {
        double r35099791 = x;
        double r35099792 = 16.0;
        double r35099793 = 116.0;
        double r35099794 = r35099792 / r35099793;
        double r35099795 = r35099791 - r35099794;
        double r35099796 = 3.0;
        double r35099797 = r35099795 * r35099796;
        double r35099798 = y;
        double r35099799 = r35099797 * r35099798;
        return r35099799;
}
↓
double f(double x, double y) {
        double r35099800 = 3.0;
        double r35099801 = y;
        double r35099802 = r35099800 * r35099801;
        double r35099803 = x;
        double r35099804 = 16.0;
        double r35099805 = 116.0;
        double r35099806 = r35099804 / r35099805;
        double r35099807 = r35099803 - r35099806;
        double r35099808 = r35099802 * r35099807;
        return r35099808;
}

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
Herbie0.3
\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)}\]

  4. Final simplification0.3

    \[\leadsto \left(3 \cdot y\right) \cdot \left(x - \frac{16}{116}\right)\]

Reproduce

herbie shell --seed 2019172 +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))