Average Error: 0.2 → 0.2
Time: 12.6s
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 r72189 = x;
        double r72190 = 16.0;
        double r72191 = 116.0;
        double r72192 = r72190 / r72191;
        double r72193 = r72189 - r72192;
        double r72194 = 3.0;
        double r72195 = r72193 * r72194;
        double r72196 = y;
        double r72197 = r72195 * r72196;
        return r72197;
}
↓
double f(double x, double y) {
        double r72198 = y;
        double r72199 = 3.0;
        double r72200 = x;
        double r72201 = r72199 * r72200;
        double r72202 = 0.41379310344827586;
        double r72203 = r72201 - r72202;
        double r72204 = r72198 * r72203;
        return r72204;
}

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 2019310 
(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))