Average Error: 0.1 → 0.1
Time: 8.2s
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 r200614 = x;
        double r200615 = y;
        double r200616 = r200614 + r200615;
        double r200617 = r200616 + r200615;
        double r200618 = r200617 + r200614;
        double r200619 = z;
        double r200620 = r200618 + r200619;
        double r200621 = r200620 + r200614;
        return r200621;
}
↓
double f(double x, double y, double z) {
        double r200622 = 3.0;
        double r200623 = x;
        double r200624 = r200622 * r200623;
        double r200625 = z;
        double r200626 = 2.0;
        double r200627 = y;
        double r200628 = r200626 * r200627;
        double r200629 = r200625 + r200628;
        double r200630 = r200624 + r200629;
        return r200630;
}

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 2020047 
(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))