Average Error: 0.2 → 0.3
Time: 10.0s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(x - \frac{16}{116}\right) \cdot \left(y \cdot 3\right)\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(x - \frac{16}{116}\right) \cdot \left(y \cdot 3\right)
double f(double x, double y) {
        double r739158 = x;
        double r739159 = 16.0;
        double r739160 = 116.0;
        double r739161 = r739159 / r739160;
        double r739162 = r739158 - r739161;
        double r739163 = 3.0;
        double r739164 = r739162 * r739163;
        double r739165 = y;
        double r739166 = r739164 * r739165;
        return r739166;
}
↓
double f(double x, double y) {
        double r739167 = x;
        double r739168 = 16.0;
        double r739169 = 116.0;
        double r739170 = r739168 / r739169;
        double r739171 = r739167 - r739170;
        double r739172 = y;
        double r739173 = 3.0;
        double r739174 = r739172 * r739173;
        double r739175 = r739171 * r739174;
        return r739175;
}

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. Simplified0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019350 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.41379310344827586))

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