Average Error: 0.2 → 0.3
Time: 15.9s
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 r54396031 = x;
        double r54396032 = 16.0;
        double r54396033 = 116.0;
        double r54396034 = r54396032 / r54396033;
        double r54396035 = r54396031 - r54396034;
        double r54396036 = 3.0;
        double r54396037 = r54396035 * r54396036;
        double r54396038 = y;
        double r54396039 = r54396037 * r54396038;
        return r54396039;
}
↓
double f(double x, double y) {
        double r54396040 = x;
        double r54396041 = 16.0;
        double r54396042 = 116.0;
        double r54396043 = r54396041 / r54396042;
        double r54396044 = r54396040 - r54396043;
        double r54396045 = 3.0;
        double r54396046 = y;
        double r54396047 = r54396045 * r54396046;
        double r54396048 = r54396044 * r54396047;
        return r54396048;
}

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 2019174 +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))