Average Error: 0.2 → 0.2
Time: 2.6s
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 r878565 = x;
        double r878566 = 16.0;
        double r878567 = 116.0;
        double r878568 = r878566 / r878567;
        double r878569 = r878565 - r878568;
        double r878570 = 3.0;
        double r878571 = r878569 * r878570;
        double r878572 = y;
        double r878573 = r878571 * r878572;
        return r878573;
}
↓
double f(double x, double y) {
        double r878574 = y;
        double r878575 = 3.0;
        double r878576 = x;
        double r878577 = r878575 * r878576;
        double r878578 = 0.41379310344827586;
        double r878579 = r878577 - r878578;
        double r878580 = r878574 * r878579;
        return r878580;
}

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 2020002 +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))