Average Error: 0.1 → 0.1
Time: 25.2s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[x \cdot 3 + \left(z + \left(y + y\right)\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
x \cdot 3 + \left(z + \left(y + y\right)\right)
double f(double x, double y, double z) {
        double r150581 = x;
        double r150582 = y;
        double r150583 = r150581 + r150582;
        double r150584 = r150583 + r150582;
        double r150585 = r150584 + r150581;
        double r150586 = z;
        double r150587 = r150585 + r150586;
        double r150588 = r150587 + r150581;
        return r150588;
}
↓
double f(double x, double y, double z) {
        double r150589 = x;
        double r150590 = 3.0;
        double r150591 = r150589 * r150590;
        double r150592 = z;
        double r150593 = y;
        double r150594 = r150593 + r150593;
        double r150595 = r150592 + r150594;
        double r150596 = r150591 + r150595;
        return r150596;
}

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. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))