Average Error: 0.1 → 0.1
Time: 19.7s
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 r7740288 = x;
        double r7740289 = y;
        double r7740290 = r7740288 + r7740289;
        double r7740291 = r7740290 + r7740289;
        double r7740292 = r7740291 + r7740288;
        double r7740293 = z;
        double r7740294 = r7740292 + r7740293;
        double r7740295 = r7740294 + r7740288;
        return r7740295;
}
↓
double f(double x, double y, double z) {
        double r7740296 = x;
        double r7740297 = 3.0;
        double r7740298 = r7740296 * r7740297;
        double r7740299 = z;
        double r7740300 = y;
        double r7740301 = r7740300 + r7740300;
        double r7740302 = r7740299 + r7740301;
        double r7740303 = r7740298 + r7740302;
        return r7740303;
}

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 2019192 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))