Average Error: 0.2 → 0.2
Time: 2.1s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(3 \cdot x - 0.4137931034482758563264326312491903081536\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(3 \cdot x - 0.4137931034482758563264326312491903081536\right) \cdot y
double f(double x, double y) {
        double r854902 = x;
        double r854903 = 16.0;
        double r854904 = 116.0;
        double r854905 = r854903 / r854904;
        double r854906 = r854902 - r854905;
        double r854907 = 3.0;
        double r854908 = r854906 * r854907;
        double r854909 = y;
        double r854910 = r854908 * r854909;
        return r854910;
}
↓
double f(double x, double y) {
        double r854911 = 3.0;
        double r854912 = x;
        double r854913 = r854911 * r854912;
        double r854914 = 0.41379310344827586;
        double r854915 = r854913 - r854914;
        double r854916 = y;
        double r854917 = r854915 * r854916;
        return r854917;
}

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

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(3 \cdot x - 0.4137931034482758563264326312491903081536\right)} \cdot y\]

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019354 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.41379310344827586))

  (* (* (- x (/ 16 116)) 3) y))