Average Error: 0.1 → 0.1
Time: 4.7s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(2 \cdot \left(x + y\right) + x\right) + z\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(2 \cdot \left(x + y\right) + x\right) + z
double f(double x, double y, double z) {
        double r167691 = x;
        double r167692 = y;
        double r167693 = r167691 + r167692;
        double r167694 = r167693 + r167692;
        double r167695 = r167694 + r167691;
        double r167696 = z;
        double r167697 = r167695 + r167696;
        double r167698 = r167697 + r167691;
        return r167698;
}
↓
double f(double x, double y, double z) {
        double r167699 = 2.0;
        double r167700 = x;
        double r167701 = y;
        double r167702 = r167700 + r167701;
        double r167703 = r167699 * r167702;
        double r167704 = r167703 + r167700;
        double r167705 = z;
        double r167706 = r167704 + r167705;
        return r167706;
}

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

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

  4. Applied associate-+r+0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020089 
(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))