Average Error: 0.1 → 0.1
Time: 16.2s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(z + 2 \cdot y\right) + 3 \cdot x\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(z + 2 \cdot y\right) + 3 \cdot x
double f(double x, double y, double z) {
        double r7023424 = x;
        double r7023425 = y;
        double r7023426 = r7023424 + r7023425;
        double r7023427 = r7023426 + r7023425;
        double r7023428 = r7023427 + r7023424;
        double r7023429 = z;
        double r7023430 = r7023428 + r7023429;
        double r7023431 = r7023430 + r7023424;
        return r7023431;
}
↓
double f(double x, double y, double z) {
        double r7023432 = z;
        double r7023433 = 2.0;
        double r7023434 = y;
        double r7023435 = r7023433 * r7023434;
        double r7023436 = r7023432 + r7023435;
        double r7023437 = 3.0;
        double r7023438 = x;
        double r7023439 = r7023437 * r7023438;
        double r7023440 = r7023436 + r7023439;
        return r7023440;
}

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

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

  3. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{3 \cdot x + \left(z + 2 \cdot y\right)}\]

  4. Final simplification0.1

    \[\leadsto \left(z + 2 \cdot y\right) + 3 \cdot x\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))