Average Error: 0.2 → 0.2
Time: 3.8s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
double f(double x, double y) {
        double r802686 = x;
        double r802687 = 16.0;
        double r802688 = 116.0;
        double r802689 = r802687 / r802688;
        double r802690 = r802686 - r802689;
        double r802691 = 3.0;
        double r802692 = r802690 * r802691;
        double r802693 = y;
        double r802694 = r802692 * r802693;
        return r802694;
}
↓
double f(double x, double y) {
        double r802695 = x;
        double r802696 = 16.0;
        double r802697 = 116.0;
        double r802698 = r802696 / r802697;
        double r802699 = r802695 - r802698;
        double r802700 = 3.0;
        double r802701 = r802699 * r802700;
        double r802702 = y;
        double r802703 = r802701 * r802702;
        return r802703;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(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))