Average Error: 0.1 → 0.1
Time: 5.1s
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 r169261 = x;
        double r169262 = y;
        double r169263 = r169261 + r169262;
        double r169264 = r169263 + r169262;
        double r169265 = r169264 + r169261;
        double r169266 = z;
        double r169267 = r169265 + r169266;
        double r169268 = r169267 + r169261;
        return r169268;
}
↓
double f(double x, double y, double z) {
        double r169269 = 3.0;
        double r169270 = x;
        double r169271 = r169269 * r169270;
        double r169272 = z;
        double r169273 = 2.0;
        double r169274 = y;
        double r169275 = r169273 * r169274;
        double r169276 = r169272 + r169275;
        double r169277 = r169271 + r169276;
        return r169277;
}

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 2020100 
(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))