Average Error: 0.1 → 0.1
Time: 15.3s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(\left(\left(x + y\right) + y\right) + x\right) + \left(z + x\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(\left(\left(x + y\right) + y\right) + x\right) + \left(z + x\right)
double f(double x, double y, double z) {
        double r144046 = x;
        double r144047 = y;
        double r144048 = r144046 + r144047;
        double r144049 = r144048 + r144047;
        double r144050 = r144049 + r144046;
        double r144051 = z;
        double r144052 = r144050 + r144051;
        double r144053 = r144052 + r144046;
        return r144053;
}
↓
double f(double x, double y, double z) {
        double r144054 = x;
        double r144055 = y;
        double r144056 = r144054 + r144055;
        double r144057 = r144056 + r144055;
        double r144058 = r144057 + r144054;
        double r144059 = z;
        double r144060 = r144059 + r144054;
        double r144061 = r144058 + r144060;
        return r144061;
}

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. Using strategy rm

  3. Applied associate-+l+0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(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))