Average Error: 0.1 → 0.1
Time: 18.5s
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 r111818 = x;
        double r111819 = y;
        double r111820 = r111818 + r111819;
        double r111821 = r111820 + r111819;
        double r111822 = r111821 + r111818;
        double r111823 = z;
        double r111824 = r111822 + r111823;
        double r111825 = r111824 + r111818;
        return r111825;
}
↓
double f(double x, double y, double z) {
        double r111826 = 2.0;
        double r111827 = x;
        double r111828 = y;
        double r111829 = r111827 + r111828;
        double r111830 = r111826 * r111829;
        double r111831 = r111830 + r111827;
        double r111832 = z;
        double r111833 = r111831 + r111832;
        return r111833;
}

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 2019298 
(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))