Average Error: 0.1 → 0.1
Time: 1.8s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[x \cdot 2 + \left(y \cdot 2 + \left(x + z\right)\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
x \cdot 2 + \left(y \cdot 2 + \left(x + z\right)\right)
double f(double x, double y, double z) {
        double r199743 = x;
        double r199744 = y;
        double r199745 = r199743 + r199744;
        double r199746 = r199745 + r199744;
        double r199747 = r199746 + r199743;
        double r199748 = z;
        double r199749 = r199747 + r199748;
        double r199750 = r199749 + r199743;
        return r199750;
}
↓
double f(double x, double y, double z) {
        double r199751 = x;
        double r199752 = 2.0;
        double r199753 = r199751 * r199752;
        double r199754 = y;
        double r199755 = r199754 * r199752;
        double r199756 = z;
        double r199757 = r199751 + r199756;
        double r199758 = r199755 + r199757;
        double r199759 = r199753 + r199758;
        return r199759;
}

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 distribute-rgt-in0.1

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

  5. Applied associate-+l+0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(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))