Average Error: 0.1 → 0.1
Time: 26.7s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[x \cdot 3 + \left(z + \left(y + y\right)\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
x \cdot 3 + \left(z + \left(y + y\right)\right)
double f(double x, double y, double z) {
        double r136097 = x;
        double r136098 = y;
        double r136099 = r136097 + r136098;
        double r136100 = r136099 + r136098;
        double r136101 = r136100 + r136097;
        double r136102 = z;
        double r136103 = r136101 + r136102;
        double r136104 = r136103 + r136097;
        return r136104;
}
↓
double f(double x, double y, double z) {
        double r136105 = x;
        double r136106 = 3.0;
        double r136107 = r136105 * r136106;
        double r136108 = z;
        double r136109 = y;
        double r136110 = r136109 + r136109;
        double r136111 = r136108 + r136110;
        double r136112 = r136107 + r136111;
        return r136112;
}

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

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))