Average Error: 0.2 → 0.2
Time: 11.3s
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 r23100695 = x;
        double r23100696 = 16.0;
        double r23100697 = 116.0;
        double r23100698 = r23100696 / r23100697;
        double r23100699 = r23100695 - r23100698;
        double r23100700 = 3.0;
        double r23100701 = r23100699 * r23100700;
        double r23100702 = y;
        double r23100703 = r23100701 * r23100702;
        return r23100703;
}
↓
double f(double x, double y) {
        double r23100704 = 3.0;
        double r23100705 = x;
        double r23100706 = r23100704 * r23100705;
        double r23100707 = 0.41379310344827586;
        double r23100708 = r23100706 - r23100707;
        double r23100709 = y;
        double r23100710 = r23100708 * r23100709;
        return r23100710;
}

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 2019179 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))