Average Error: 0.2 → 0.2
Time: 13.4s
Precision: 64
\[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]
↓
\[\left(3.0 \cdot x - 0.41379310344827586\right) \cdot y\]
\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y
↓
\left(3.0 \cdot x - 0.41379310344827586\right) \cdot y
double f(double x, double y) {
        double r46817914 = x;
        double r46817915 = 16.0;
        double r46817916 = 116.0;
        double r46817917 = r46817915 / r46817916;
        double r46817918 = r46817914 - r46817917;
        double r46817919 = 3.0;
        double r46817920 = r46817918 * r46817919;
        double r46817921 = y;
        double r46817922 = r46817920 * r46817921;
        return r46817922;
}
↓
double f(double x, double y) {
        double r46817923 = 3.0;
        double r46817924 = x;
        double r46817925 = r46817923 * r46817924;
        double r46817926 = 0.41379310344827586;
        double r46817927 = r46817925 - r46817926;
        double r46817928 = y;
        double r46817929 = r46817927 * r46817928;
        return r46817929;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019163 
(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))