Average Error: 0.2 → 0.3
Time: 13.2s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)
double f(double x, double y) {
        double r598921 = x;
        double r598922 = 16.0;
        double r598923 = 116.0;
        double r598924 = r598922 / r598923;
        double r598925 = r598921 - r598924;
        double r598926 = 3.0;
        double r598927 = r598925 * r598926;
        double r598928 = y;
        double r598929 = r598927 * r598928;
        return r598929;
}
↓
double f(double x, double y) {
        double r598930 = x;
        double r598931 = 16.0;
        double r598932 = 116.0;
        double r598933 = r598931 / r598932;
        double r598934 = r598930 - r598933;
        double r598935 = 3.0;
        double r598936 = y;
        double r598937 = r598935 * r598936;
        double r598938 = r598934 * r598937;
        return r598938;
}

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
Herbie0.3
\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)}\]

  4. Final simplification0.3

    \[\leadsto \left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)\]

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.413793103448275856))

  (* (* (- x (/ 16 116)) 3) y))