Average Error: 0.2 → 0.2
Time: 13.4s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(3 \cdot x - 0.4137931034482758563264326312491903081536\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(3 \cdot x - 0.4137931034482758563264326312491903081536\right) \cdot y
double f(double x, double y) {
        double r617363 = x;
        double r617364 = 16.0;
        double r617365 = 116.0;
        double r617366 = r617364 / r617365;
        double r617367 = r617363 - r617366;
        double r617368 = 3.0;
        double r617369 = r617367 * r617368;
        double r617370 = y;
        double r617371 = r617369 * r617370;
        return r617371;
}
↓
double f(double x, double y) {
        double r617372 = 3.0;
        double r617373 = x;
        double r617374 = r617372 * r617373;
        double r617375 = 0.41379310344827586;
        double r617376 = r617374 - r617375;
        double r617377 = y;
        double r617378 = r617376 * r617377;
        return r617378;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

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

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