Average Error: 0.2 → 0.2
Time: 46.5s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)
double f(double x, double y) {
        double r43327851 = x;
        double r43327852 = 16.0;
        double r43327853 = 116.0;
        double r43327854 = r43327852 / r43327853;
        double r43327855 = r43327851 - r43327854;
        double r43327856 = 3.0;
        double r43327857 = r43327855 * r43327856;
        double r43327858 = y;
        double r43327859 = r43327857 * r43327858;
        return r43327859;
}
↓
double f(double x, double y) {
        double r43327860 = y;
        double r43327861 = x;
        double r43327862 = 3.0;
        double r43327863 = r43327861 * r43327862;
        double r43327864 = 0.41379310344827586;
        double r43327865 = r43327863 - r43327864;
        double r43327866 = r43327860 * r43327865;
        return r43327866;
}

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

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

Reproduce

herbie shell --seed 2019200 
(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))