Average Error: 0.2 → 0.2
Time: 8.6s
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 r536277 = x;
        double r536278 = 16.0;
        double r536279 = 116.0;
        double r536280 = r536278 / r536279;
        double r536281 = r536277 - r536280;
        double r536282 = 3.0;
        double r536283 = r536281 * r536282;
        double r536284 = y;
        double r536285 = r536283 * r536284;
        return r536285;
}
↓
double f(double x, double y) {
        double r536286 = 3.0;
        double r536287 = x;
        double r536288 = r536286 * r536287;
        double r536289 = 0.41379310344827586;
        double r536290 = r536288 - r536289;
        double r536291 = y;
        double r536292 = r536290 * r536291;
        return r536292;
}

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 2019291 
(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))