Average Error: 0.1 → 0.1
Time: 17.5s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(2 \cdot \left(x + y\right) + x\right) + z\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(2 \cdot \left(x + y\right) + x\right) + z
double f(double x, double y, double z) {
        double r91916 = x;
        double r91917 = y;
        double r91918 = r91916 + r91917;
        double r91919 = r91918 + r91917;
        double r91920 = r91919 + r91916;
        double r91921 = z;
        double r91922 = r91920 + r91921;
        double r91923 = r91922 + r91916;
        return r91923;
}
↓
double f(double x, double y, double z) {
        double r91924 = 2.0;
        double r91925 = x;
        double r91926 = y;
        double r91927 = r91925 + r91926;
        double r91928 = r91924 * r91927;
        double r91929 = r91928 + r91925;
        double r91930 = z;
        double r91931 = r91929 + r91930;
        return r91931;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]

  2. Simplified0.1

    \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)}\]
  3. Using strategy rm

  4. Applied associate-+r+0.1

    \[\leadsto \color{blue}{\left(2 \cdot \left(x + y\right) + x\right) + z}\]

  5. Final simplification0.1

    \[\leadsto \left(2 \cdot \left(x + y\right) + x\right) + z\]

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  :precision binary64
  (+ (+ (+ (+ (+ x y) y) x) z) x))