Average Error: 0.1 → 0.1
Time: 6.4s
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 r139620 = x;
        double r139621 = y;
        double r139622 = r139620 + r139621;
        double r139623 = r139622 + r139621;
        double r139624 = r139623 + r139620;
        double r139625 = z;
        double r139626 = r139624 + r139625;
        double r139627 = r139626 + r139620;
        return r139627;
}
↓
double f(double x, double y, double z) {
        double r139628 = 3.0;
        double r139629 = x;
        double r139630 = r139628 * r139629;
        double r139631 = z;
        double r139632 = 2.0;
        double r139633 = y;
        double r139634 = r139632 * r139633;
        double r139635 = r139631 + r139634;
        double r139636 = r139630 + r139635;
        return r139636;
}

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 2020001 
(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))