Average Error: 0.2 → 0.2
Time: 2.3s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(3 \cdot x - 0.413793103448275856\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(3 \cdot x - 0.413793103448275856\right) \cdot y
double f(double x, double y) {
        double r884843 = x;
        double r884844 = 16.0;
        double r884845 = 116.0;
        double r884846 = r884844 / r884845;
        double r884847 = r884843 - r884846;
        double r884848 = 3.0;
        double r884849 = r884847 * r884848;
        double r884850 = y;
        double r884851 = r884849 * r884850;
        return r884851;
}
↓
double f(double x, double y) {
        double r884852 = 3.0;
        double r884853 = x;
        double r884854 = r884852 * r884853;
        double r884855 = 0.41379310344827586;
        double r884856 = r884854 - r884855;
        double r884857 = y;
        double r884858 = r884856 * r884857;
        return r884858;
}

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
\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

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

    \[\leadsto \color{blue}{\left(3 \cdot x - 0.413793103448275856\right)} \cdot y\]

  3. Final simplification0.2

    \[\leadsto \left(3 \cdot x - 0.413793103448275856\right) \cdot y\]

Reproduce

herbie shell --seed 2020062 
(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))