Average Error: 0.3 → 0.3
Time: 17.3s
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 r552784 = x;
        double r552785 = 16.0;
        double r552786 = 116.0;
        double r552787 = r552785 / r552786;
        double r552788 = r552784 - r552787;
        double r552789 = 3.0;
        double r552790 = r552788 * r552789;
        double r552791 = y;
        double r552792 = r552790 * r552791;
        return r552792;
}
↓
double f(double x, double y) {
        double r552793 = 3.0;
        double r552794 = x;
        double r552795 = r552793 * r552794;
        double r552796 = 0.41379310344827586;
        double r552797 = r552795 - r552796;
        double r552798 = y;
        double r552799 = r552797 * r552798;
        return r552799;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.3
Herbie0.3
\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

Derivation

  1. Initial program 0.3

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

  2. Taylor expanded around 0 0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(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))