Average Error: 0.1 → 0.1
Time: 4.2s
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 r184754 = x;
        double r184755 = y;
        double r184756 = r184754 + r184755;
        double r184757 = r184756 + r184755;
        double r184758 = r184757 + r184754;
        double r184759 = z;
        double r184760 = r184758 + r184759;
        double r184761 = r184760 + r184754;
        return r184761;
}
↓
double f(double x, double y, double z) {
        double r184762 = 2.0;
        double r184763 = x;
        double r184764 = y;
        double r184765 = r184763 + r184764;
        double r184766 = r184762 * r184765;
        double r184767 = r184766 + r184763;
        double r184768 = z;
        double r184769 = r184767 + r184768;
        return r184769;
}

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 2020018 
(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))