Average Error: 0.1 → 0.1
Time: 17.4s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(\left(y + y\right) + z\right) + 3 \cdot x\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(\left(y + y\right) + z\right) + 3 \cdot x
double f(double x, double y, double z) {
        double r7828197 = x;
        double r7828198 = y;
        double r7828199 = r7828197 + r7828198;
        double r7828200 = r7828199 + r7828198;
        double r7828201 = r7828200 + r7828197;
        double r7828202 = z;
        double r7828203 = r7828201 + r7828202;
        double r7828204 = r7828203 + r7828197;
        return r7828204;
}
↓
double f(double x, double y, double z) {
        double r7828205 = y;
        double r7828206 = r7828205 + r7828205;
        double r7828207 = z;
        double r7828208 = r7828206 + r7828207;
        double r7828209 = 3.0;
        double r7828210 = x;
        double r7828211 = r7828209 * r7828210;
        double r7828212 = r7828208 + r7828211;
        return r7828212;
}

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

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))