Average Error: 0.1 → 0.1
Time: 8.4s
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 r153766 = x;
        double r153767 = y;
        double r153768 = r153766 + r153767;
        double r153769 = r153768 + r153767;
        double r153770 = r153769 + r153766;
        double r153771 = z;
        double r153772 = r153770 + r153771;
        double r153773 = r153772 + r153766;
        return r153773;
}
↓
double f(double x, double y, double z) {
        double r153774 = 2.0;
        double r153775 = x;
        double r153776 = y;
        double r153777 = r153775 + r153776;
        double r153778 = r153774 * r153777;
        double r153779 = r153778 + r153775;
        double r153780 = z;
        double r153781 = r153779 + r153780;
        return r153781;
}

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 *-un-lft-identity0.1

    \[\leadsto \left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + \color{blue}{1 \cdot x}\]

  4. Applied *-un-lft-identity0.1

    \[\leadsto \color{blue}{1 \cdot \left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right)} + 1 \cdot x\]

  5. Applied distribute-lft-out0.1

    \[\leadsto \color{blue}{1 \cdot \left(\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\right)}\]

  6. Simplified0.1

    \[\leadsto 1 \cdot \color{blue}{\left(\left(2 \cdot \left(x + y\right) + x\right) + z\right)}\]

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019308 
(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))