Average Error: 0.2 → 0.3
Time: 20.9s
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 r36341164 = x;
        double r36341165 = 16.0;
        double r36341166 = 116.0;
        double r36341167 = r36341165 / r36341166;
        double r36341168 = r36341164 - r36341167;
        double r36341169 = 3.0;
        double r36341170 = r36341168 * r36341169;
        double r36341171 = y;
        double r36341172 = r36341170 * r36341171;
        return r36341172;
}
↓
double f(double x, double y) {
        double r36341173 = 3.0;
        double r36341174 = y;
        double r36341175 = r36341173 * r36341174;
        double r36341176 = x;
        double r36341177 = 16.0;
        double r36341178 = 116.0;
        double r36341179 = r36341177 / r36341178;
        double r36341180 = r36341176 - r36341179;
        double r36341181 = r36341175 * r36341180;
        return r36341181;
}

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 2019172 +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))