Average Error: 0.1 → 0.1
Time: 16.0s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(\left(y + y\right) + z\right) + 3 \cdot x\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(\left(y + y\right) + z\right) + 3 \cdot x
double f(double x, double y, double z) {
        double r7899066 = x;
        double r7899067 = y;
        double r7899068 = r7899066 + r7899067;
        double r7899069 = r7899068 + r7899067;
        double r7899070 = r7899069 + r7899066;
        double r7899071 = z;
        double r7899072 = r7899070 + r7899071;
        double r7899073 = r7899072 + r7899066;
        return r7899073;
}
↓
double f(double x, double y, double z) {
        double r7899074 = y;
        double r7899075 = r7899074 + r7899074;
        double r7899076 = z;
        double r7899077 = r7899075 + r7899076;
        double r7899078 = 3.0;
        double r7899079 = x;
        double r7899080 = r7899078 * r7899079;
        double r7899081 = r7899077 + r7899080;
        return r7899081;
}

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

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

    \[\leadsto \color{blue}{\left(\left(y + y\right) + z\right) + 3 \cdot x}\]

  5. Final simplification0.1

    \[\leadsto \left(\left(y + y\right) + z\right) + 3 \cdot x\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))