Average Error: 0.2 → 0.2
Time: 3.4s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[y \cdot \left(3 \cdot x - 0.4137931034482758563264326312491903081536\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
y \cdot \left(3 \cdot x - 0.4137931034482758563264326312491903081536\right)
double f(double x, double y) {
        double r823664 = x;
        double r823665 = 16.0;
        double r823666 = 116.0;
        double r823667 = r823665 / r823666;
        double r823668 = r823664 - r823667;
        double r823669 = 3.0;
        double r823670 = r823668 * r823669;
        double r823671 = y;
        double r823672 = r823670 * r823671;
        return r823672;
}
↓
double f(double x, double y) {
        double r823673 = y;
        double r823674 = 3.0;
        double r823675 = x;
        double r823676 = r823674 * r823675;
        double r823677 = 0.41379310344827586;
        double r823678 = r823676 - r823677;
        double r823679 = r823673 * r823678;
        return r823679;
}

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
\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]

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

    \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right) - 0.4137931034482758563264326312491903081536 \cdot y}\]

  3. Simplified0.2

    \[\leadsto \color{blue}{y \cdot \left(3 \cdot x - 0.4137931034482758563264326312491903081536\right)}\]

  4. Final simplification0.2

    \[\leadsto y \cdot \left(3 \cdot x - 0.4137931034482758563264326312491903081536\right)\]

Reproduce

herbie shell --seed 2019322 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.413793103448275856))

  (* (* (- x (/ 16 116)) 3) y))