Average Error: 0.1 → 0.1
Time: 42.2s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(z + \left(y + y\right)\right) + 3 \cdot x\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(z + \left(y + y\right)\right) + 3 \cdot x
double f(double x, double y, double z) {
        double r9680296 = x;
        double r9680297 = y;
        double r9680298 = r9680296 + r9680297;
        double r9680299 = r9680298 + r9680297;
        double r9680300 = r9680299 + r9680296;
        double r9680301 = z;
        double r9680302 = r9680300 + r9680301;
        double r9680303 = r9680302 + r9680296;
        return r9680303;
}
↓
double f(double x, double y, double z) {
        double r9680304 = z;
        double r9680305 = y;
        double r9680306 = r9680305 + r9680305;
        double r9680307 = r9680304 + r9680306;
        double r9680308 = 3.0;
        double r9680309 = x;
        double r9680310 = r9680308 * r9680309;
        double r9680311 = r9680307 + r9680310;
        return r9680311;
}

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

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))