Average Error: 0.1 → 0.1
Time: 11.5s
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 r123460 = x;
        double r123461 = y;
        double r123462 = r123460 + r123461;
        double r123463 = r123462 + r123461;
        double r123464 = r123463 + r123460;
        double r123465 = z;
        double r123466 = r123464 + r123465;
        double r123467 = r123466 + r123460;
        return r123467;
}
↓
double f(double x, double y, double z) {
        double r123468 = 3.0;
        double r123469 = x;
        double r123470 = r123468 * r123469;
        double r123471 = z;
        double r123472 = 2.0;
        double r123473 = y;
        double r123474 = r123472 * r123473;
        double r123475 = r123471 + r123474;
        double r123476 = r123470 + r123475;
        return r123476;
}

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

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

  3. Taylor expanded around 0 0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(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))