Average Error: 0.1 → 0.1
Time: 41.5s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[3 \cdot x + \left(z + \left(y + y\right)\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
3 \cdot x + \left(z + \left(y + y\right)\right)
double f(double x, double y, double z) {
        double r10065164 = x;
        double r10065165 = y;
        double r10065166 = r10065164 + r10065165;
        double r10065167 = r10065166 + r10065165;
        double r10065168 = r10065167 + r10065164;
        double r10065169 = z;
        double r10065170 = r10065168 + r10065169;
        double r10065171 = r10065170 + r10065164;
        return r10065171;
}
↓
double f(double x, double y, double z) {
        double r10065172 = 3.0;
        double r10065173 = x;
        double r10065174 = r10065172 * r10065173;
        double r10065175 = z;
        double r10065176 = y;
        double r10065177 = r10065176 + r10065176;
        double r10065178 = r10065175 + r10065177;
        double r10065179 = r10065174 + r10065178;
        return r10065179;
}

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

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))