Average Error: 0.2 → 0.2
Time: 14.5s
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 r639458 = x;
        double r639459 = 16.0;
        double r639460 = 116.0;
        double r639461 = r639459 / r639460;
        double r639462 = r639458 - r639461;
        double r639463 = 3.0;
        double r639464 = r639462 * r639463;
        double r639465 = y;
        double r639466 = r639464 * r639465;
        return r639466;
}
↓
double f(double x, double y) {
        double r639467 = y;
        double r639468 = 3.0;
        double r639469 = x;
        double r639470 = r639468 * r639469;
        double r639471 = 0.41379310344827586;
        double r639472 = r639470 - r639471;
        double r639473 = r639467 * r639472;
        return r639473;
}

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 2019306 
(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))