Average Error: 0.2 → 0.2
Time: 14.4s
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 r519345 = x;
        double r519346 = 16.0;
        double r519347 = 116.0;
        double r519348 = r519346 / r519347;
        double r519349 = r519345 - r519348;
        double r519350 = 3.0;
        double r519351 = r519349 * r519350;
        double r519352 = y;
        double r519353 = r519351 * r519352;
        return r519353;
}
↓
double f(double x, double y) {
        double r519354 = 3.0;
        double r519355 = x;
        double r519356 = r519354 * r519355;
        double r519357 = 0.41379310344827586;
        double r519358 = r519356 - r519357;
        double r519359 = y;
        double r519360 = r519358 * r519359;
        return r519360;
}

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 2019322 
(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))