Average Error: 0.2 → 0.2
Time: 1.9s
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 r1023536 = x;
        double r1023537 = 16.0;
        double r1023538 = 116.0;
        double r1023539 = r1023537 / r1023538;
        double r1023540 = r1023536 - r1023539;
        double r1023541 = 3.0;
        double r1023542 = r1023540 * r1023541;
        double r1023543 = y;
        double r1023544 = r1023542 * r1023543;
        return r1023544;
}
↓
double f(double x, double y) {
        double r1023545 = 3.0;
        double r1023546 = x;
        double r1023547 = r1023545 * r1023546;
        double r1023548 = 0.41379310344827586;
        double r1023549 = r1023547 - r1023548;
        double r1023550 = y;
        double r1023551 = r1023549 * r1023550;
        return r1023551;
}

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 2019354 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.41379310344827586))

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