Average Error: 0.1 → 0.1
Time: 3.5s
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 r144912 = x;
        double r144913 = y;
        double r144914 = r144912 + r144913;
        double r144915 = r144914 + r144913;
        double r144916 = r144915 + r144912;
        double r144917 = z;
        double r144918 = r144916 + r144917;
        double r144919 = r144918 + r144912;
        return r144919;
}
↓
double f(double x, double y, double z) {
        double r144920 = 2.0;
        double r144921 = x;
        double r144922 = y;
        double r144923 = r144921 + r144922;
        double r144924 = r144920 * r144923;
        double r144925 = r144924 + r144921;
        double r144926 = z;
        double r144927 = r144925 + r144926;
        return r144927;
}

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 2019354 
(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))