Average Error: 0.1 → 0.1
Time: 44.0s
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 r157164 = x;
        double r157165 = y;
        double r157166 = r157164 + r157165;
        double r157167 = r157166 + r157165;
        double r157168 = r157167 + r157164;
        double r157169 = z;
        double r157170 = r157168 + r157169;
        double r157171 = r157170 + r157164;
        return r157171;
}
↓
double f(double x, double y, double z) {
        double r157172 = 3.0;
        double r157173 = x;
        double r157174 = r157172 * r157173;
        double r157175 = z;
        double r157176 = 2.0;
        double r157177 = y;
        double r157178 = r157176 * r157177;
        double r157179 = r157175 + r157178;
        double r157180 = r157174 + r157179;
        return r157180;
}

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 2020045 
(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))