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 r867994 = x;
        double r867995 = 16.0;
        double r867996 = 116.0;
        double r867997 = r867995 / r867996;
        double r867998 = r867994 - r867997;
        double r867999 = 3.0;
        double r868000 = r867998 * r867999;
        double r868001 = y;
        double r868002 = r868000 * r868001;
        return r868002;
}
↓
double f(double x, double y) {
        double r868003 = y;
        double r868004 = 3.0;
        double r868005 = x;
        double r868006 = r868004 * r868005;
        double r868007 = 0.41379310344827586;
        double r868008 = r868006 - r868007;
        double r868009 = r868003 * r868008;
        return r868009;
}

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 
(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))