Average Error: 0.1 → 0.1
Time: 22.1s
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 r9286646 = x;
        double r9286647 = y;
        double r9286648 = r9286646 + r9286647;
        double r9286649 = r9286648 + r9286647;
        double r9286650 = r9286649 + r9286646;
        double r9286651 = z;
        double r9286652 = r9286650 + r9286651;
        double r9286653 = r9286652 + r9286646;
        return r9286653;
}
↓
double f(double x, double y, double z) {
        double r9286654 = y;
        double r9286655 = r9286654 + r9286654;
        double r9286656 = z;
        double r9286657 = r9286655 + r9286656;
        double r9286658 = 3.0;
        double r9286659 = x;
        double r9286660 = r9286658 * r9286659;
        double r9286661 = r9286657 + r9286660;
        return r9286661;
}

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 2019168 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))