Average Error: 0.2 → 0.3
Time: 40.2s
Precision: 64
\[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]
↓
\[\left(3.0 \cdot y\right) \cdot \left(x - \frac{16.0}{116.0}\right)\]
\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y
↓
\left(3.0 \cdot y\right) \cdot \left(x - \frac{16.0}{116.0}\right)
double f(double x, double y) {
        double r42529110 = x;
        double r42529111 = 16.0;
        double r42529112 = 116.0;
        double r42529113 = r42529111 / r42529112;
        double r42529114 = r42529110 - r42529113;
        double r42529115 = 3.0;
        double r42529116 = r42529114 * r42529115;
        double r42529117 = y;
        double r42529118 = r42529116 * r42529117;
        return r42529118;
}
↓
double f(double x, double y) {
        double r42529119 = 3.0;
        double r42529120 = y;
        double r42529121 = r42529119 * r42529120;
        double r42529122 = x;
        double r42529123 = 16.0;
        double r42529124 = 116.0;
        double r42529125 = r42529123 / r42529124;
        double r42529126 = r42529122 - r42529125;
        double r42529127 = r42529121 * r42529126;
        return r42529127;
}

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
\[y \cdot \left(x \cdot 3.0 - 0.41379310344827586\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\left(x - \frac{16.0}{116.0}\right) \cdot \left(3.0 \cdot y\right)}\]

  4. Final simplification0.3

    \[\leadsto \left(3.0 \cdot y\right) \cdot \left(x - \frac{16.0}{116.0}\right)\]

Reproduce

herbie shell --seed 2019165 
(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))