Average Error: 0.1 → 0.1
Time: 12.1s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[3 \cdot x + \left(z + 2 \cdot y\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
3 \cdot x + \left(z + 2 \cdot y\right)
double f(double x, double y, double z) {
        double r195973 = x;
        double r195974 = y;
        double r195975 = r195973 + r195974;
        double r195976 = r195975 + r195974;
        double r195977 = r195976 + r195973;
        double r195978 = z;
        double r195979 = r195977 + r195978;
        double r195980 = r195979 + r195973;
        return r195980;
}
↓
double f(double x, double y, double z) {
        double r195981 = 3.0;
        double r195982 = x;
        double r195983 = r195981 * r195982;
        double r195984 = z;
        double r195985 = 2.0;
        double r195986 = y;
        double r195987 = r195985 * r195986;
        double r195988 = r195984 + r195987;
        double r195989 = r195983 + r195988;
        return r195989;
}

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

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

  3. Taylor expanded around 0 0.1

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

  4. Final simplification0.1

    \[\leadsto 3 \cdot x + \left(z + 2 \cdot y\right)\]

Reproduce

herbie shell --seed 2019326 
(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))