Average Error: 0.1 → 0.1
Time: 6.1s
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 r197262 = x;
        double r197263 = y;
        double r197264 = r197262 + r197263;
        double r197265 = r197264 + r197263;
        double r197266 = r197265 + r197262;
        double r197267 = z;
        double r197268 = r197266 + r197267;
        double r197269 = r197268 + r197262;
        return r197269;
}
↓
double f(double x, double y, double z) {
        double r197270 = 3.0;
        double r197271 = x;
        double r197272 = r197270 * r197271;
        double r197273 = z;
        double r197274 = 2.0;
        double r197275 = y;
        double r197276 = r197274 * r197275;
        double r197277 = r197273 + r197276;
        double r197278 = r197272 + r197277;
        return r197278;
}

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 2020083 
(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))