Average Error: 0.2 → 0.3
Time: 13.6s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[3 \cdot \left(\left(x - \frac{16}{116}\right) \cdot y\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
3 \cdot \left(\left(x - \frac{16}{116}\right) \cdot y\right)
double f(double x, double y) {
        double r581865 = x;
        double r581866 = 16.0;
        double r581867 = 116.0;
        double r581868 = r581866 / r581867;
        double r581869 = r581865 - r581868;
        double r581870 = 3.0;
        double r581871 = r581869 * r581870;
        double r581872 = y;
        double r581873 = r581871 * r581872;
        return r581873;
}
↓
double f(double x, double y) {
        double r581874 = 3.0;
        double r581875 = x;
        double r581876 = 16.0;
        double r581877 = 116.0;
        double r581878 = r581876 / r581877;
        double r581879 = r581875 - r581878;
        double r581880 = y;
        double r581881 = r581879 * r581880;
        double r581882 = r581874 * r581881;
        return r581882;
}

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. Simplified0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 +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))