Average Error: 0.1 → 0.1
Time: 7.6s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[x + \left(z + \left(y + x\right) \cdot 2\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
x + \left(z + \left(y + x\right) \cdot 2\right)
double f(double x, double y, double z) {
        double r133834 = x;
        double r133835 = y;
        double r133836 = r133834 + r133835;
        double r133837 = r133836 + r133835;
        double r133838 = r133837 + r133834;
        double r133839 = z;
        double r133840 = r133838 + r133839;
        double r133841 = r133840 + r133834;
        return r133841;
}
↓
double f(double x, double y, double z) {
        double r133842 = x;
        double r133843 = z;
        double r133844 = y;
        double r133845 = r133844 + r133842;
        double r133846 = 2.0;
        double r133847 = r133845 * r133846;
        double r133848 = r133843 + r133847;
        double r133849 = r133842 + r133848;
        return r133849;
}

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. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))