Average Error: 0.2 → 0.3
Time: 16.7s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(3 \cdot y\right) \cdot \left(x - \frac{16}{116}\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(3 \cdot y\right) \cdot \left(x - \frac{16}{116}\right)
double f(double x, double y) {
        double r36927879 = x;
        double r36927880 = 16.0;
        double r36927881 = 116.0;
        double r36927882 = r36927880 / r36927881;
        double r36927883 = r36927879 - r36927882;
        double r36927884 = 3.0;
        double r36927885 = r36927883 * r36927884;
        double r36927886 = y;
        double r36927887 = r36927885 * r36927886;
        return r36927887;
}
↓
double f(double x, double y) {
        double r36927888 = 3.0;
        double r36927889 = y;
        double r36927890 = r36927888 * r36927889;
        double r36927891 = x;
        double r36927892 = 16.0;
        double r36927893 = 116.0;
        double r36927894 = r36927892 / r36927893;
        double r36927895 = r36927891 - r36927894;
        double r36927896 = r36927890 * r36927895;
        return r36927896;
}

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

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

Reproduce

herbie shell --seed 2019192 +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))