Average Error: 0.1 → 0.1
Time: 18.1s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(\left(y + y\right) + 3 \cdot x\right) + z\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(\left(y + y\right) + 3 \cdot x\right) + z
double f(double x, double y, double z) {
        double r6609283 = x;
        double r6609284 = y;
        double r6609285 = r6609283 + r6609284;
        double r6609286 = r6609285 + r6609284;
        double r6609287 = r6609286 + r6609283;
        double r6609288 = z;
        double r6609289 = r6609287 + r6609288;
        double r6609290 = r6609289 + r6609283;
        return r6609290;
}
↓
double f(double x, double y, double z) {
        double r6609291 = y;
        double r6609292 = r6609291 + r6609291;
        double r6609293 = 3.0;
        double r6609294 = x;
        double r6609295 = r6609293 * r6609294;
        double r6609296 = r6609292 + r6609295;
        double r6609297 = z;
        double r6609298 = r6609296 + r6609297;
        return r6609298;
}

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

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))