Average Error: 0.1 → 0.1
Time: 8.7s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[3 \cdot x + \left(z + 2 \cdot y\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
3 \cdot x + \left(z + 2 \cdot y\right)
double f(double x, double y, double z) {
        double r170555 = x;
        double r170556 = y;
        double r170557 = r170555 + r170556;
        double r170558 = r170557 + r170556;
        double r170559 = r170558 + r170555;
        double r170560 = z;
        double r170561 = r170559 + r170560;
        double r170562 = r170561 + r170555;
        return r170562;
}
↓
double f(double x, double y, double z) {
        double r170563 = 3.0;
        double r170564 = x;
        double r170565 = r170563 * r170564;
        double r170566 = z;
        double r170567 = 2.0;
        double r170568 = y;
        double r170569 = r170567 * r170568;
        double r170570 = r170566 + r170569;
        double r170571 = r170565 + r170570;
        return r170571;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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))