Average Error: 0.2 → 0.2
Time: 2.4s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[y \cdot \left(3 \cdot x - 0.413793103448275856\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
y \cdot \left(3 \cdot x - 0.413793103448275856\right)
double f(double x, double y) {
        double r755049 = x;
        double r755050 = 16.0;
        double r755051 = 116.0;
        double r755052 = r755050 / r755051;
        double r755053 = r755049 - r755052;
        double r755054 = 3.0;
        double r755055 = r755053 * r755054;
        double r755056 = y;
        double r755057 = r755055 * r755056;
        return r755057;
}
↓
double f(double x, double y) {
        double r755058 = y;
        double r755059 = 3.0;
        double r755060 = x;
        double r755061 = r755059 * r755060;
        double r755062 = 0.41379310344827586;
        double r755063 = r755061 - r755062;
        double r755064 = r755058 * r755063;
        return r755064;
}

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
\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

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

    \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right) - 0.413793103448275856 \cdot y}\]

  3. Simplified0.2

    \[\leadsto \color{blue}{y \cdot \left(3 \cdot x - 0.413793103448275856\right)}\]

  4. Final simplification0.2

    \[\leadsto y \cdot \left(3 \cdot x - 0.413793103448275856\right)\]

Reproduce

herbie shell --seed 2020064 
(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))