Average Error: 0.2 → 0.3
Time: 22.2s
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 r229682828 = x;
        double r229682829 = 16.0;
        double r229682830 = 116.0;
        double r229682831 = r229682829 / r229682830;
        double r229682832 = r229682828 - r229682831;
        double r229682833 = 3.0;
        double r229682834 = r229682832 * r229682833;
        double r229682835 = y;
        double r229682836 = r229682834 * r229682835;
        return r229682836;
}
↓
double f(double x, double y) {
        double r229682837 = x;
        double r229682838 = 16.0;
        double r229682839 = 116.0;
        double r229682840 = r229682838 / r229682839;
        double r229682841 = r229682837 - r229682840;
        double r229682842 = 3.0;
        double r229682843 = y;
        double r229682844 = r229682842 * r229682843;
        double r229682845 = r229682841 * r229682844;
        return r229682845;
}

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 2019173 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))