Average Error: 0.1 → 0.1
Time: 5.3s
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 r180861 = x;
        double r180862 = y;
        double r180863 = r180861 + r180862;
        double r180864 = r180863 + r180862;
        double r180865 = r180864 + r180861;
        double r180866 = z;
        double r180867 = r180865 + r180866;
        double r180868 = r180867 + r180861;
        return r180868;
}
↓
double f(double x, double y, double z) {
        double r180869 = 2.0;
        double r180870 = x;
        double r180871 = y;
        double r180872 = r180870 + r180871;
        double r180873 = r180869 * r180872;
        double r180874 = r180873 + r180870;
        double r180875 = z;
        double r180876 = r180874 + r180875;
        return r180876;
}

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 2020034 
(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))