Average Error: 0.2 → 0.2
Time: 2.4s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[y \cdot \left(3 \cdot x - 0.413793103448275856\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
y \cdot \left(3 \cdot x - 0.413793103448275856\right)
double f(double x, double y) {
        double r882767 = x;
        double r882768 = 16.0;
        double r882769 = 116.0;
        double r882770 = r882768 / r882769;
        double r882771 = r882767 - r882770;
        double r882772 = 3.0;
        double r882773 = r882771 * r882772;
        double r882774 = y;
        double r882775 = r882773 * r882774;
        return r882775;
}
↓
double f(double x, double y) {
        double r882776 = y;
        double r882777 = 3.0;
        double r882778 = x;
        double r882779 = r882777 * r882778;
        double r882780 = 0.41379310344827586;
        double r882781 = r882779 - r882780;
        double r882782 = r882776 * r882781;
        return r882782;
}

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

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020065 +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))