Average Error: 0.1 → 0.1
Time: 4.5s
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 r215058 = x;
        double r215059 = y;
        double r215060 = r215058 + r215059;
        double r215061 = r215060 + r215059;
        double r215062 = r215061 + r215058;
        double r215063 = z;
        double r215064 = r215062 + r215063;
        double r215065 = r215064 + r215058;
        return r215065;
}
↓
double f(double x, double y, double z) {
        double r215066 = 2.0;
        double r215067 = x;
        double r215068 = y;
        double r215069 = r215067 + r215068;
        double r215070 = r215066 * r215069;
        double r215071 = r215070 + r215067;
        double r215072 = z;
        double r215073 = r215071 + r215072;
        return r215073;
}

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 2020001 
(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))