Average Error: 0.2 → 0.2
Time: 2.7s
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 r927739 = x;
        double r927740 = 16.0;
        double r927741 = 116.0;
        double r927742 = r927740 / r927741;
        double r927743 = r927739 - r927742;
        double r927744 = 3.0;
        double r927745 = r927743 * r927744;
        double r927746 = y;
        double r927747 = r927745 * r927746;
        return r927747;
}
↓
double f(double x, double y) {
        double r927748 = 3.0;
        double r927749 = x;
        double r927750 = r927748 * r927749;
        double r927751 = 0.41379310344827586;
        double r927752 = r927750 - r927751;
        double r927753 = y;
        double r927754 = r927752 * r927753;
        return r927754;
}

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 2020021 
(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))