Average Error: 0.1 → 0.1
Time: 5.6s
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 r185663 = x;
        double r185664 = y;
        double r185665 = r185663 + r185664;
        double r185666 = r185665 + r185664;
        double r185667 = r185666 + r185663;
        double r185668 = z;
        double r185669 = r185667 + r185668;
        double r185670 = r185669 + r185663;
        return r185670;
}
↓
double f(double x, double y, double z) {
        double r185671 = 2.0;
        double r185672 = x;
        double r185673 = y;
        double r185674 = r185672 + r185673;
        double r185675 = r185671 * r185674;
        double r185676 = r185675 + r185672;
        double r185677 = z;
        double r185678 = r185676 + r185677;
        return r185678;
}

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 2020003 
(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))