Average Error: 0.2 → 0.2
Time: 3.2s
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 r1062023 = x;
        double r1062024 = 16.0;
        double r1062025 = 116.0;
        double r1062026 = r1062024 / r1062025;
        double r1062027 = r1062023 - r1062026;
        double r1062028 = 3.0;
        double r1062029 = r1062027 * r1062028;
        double r1062030 = y;
        double r1062031 = r1062029 * r1062030;
        return r1062031;
}
↓
double f(double x, double y) {
        double r1062032 = y;
        double r1062033 = 3.0;
        double r1062034 = x;
        double r1062035 = r1062033 * r1062034;
        double r1062036 = 0.41379310344827586;
        double r1062037 = r1062035 - r1062036;
        double r1062038 = r1062032 * r1062037;
        return r1062038;
}

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 2020057 
(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))