Average Error: 0.1 → 0.1
Time: 17.9s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(\left(y + y\right) + 3 \cdot x\right) + z\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(\left(y + y\right) + 3 \cdot x\right) + z
double f(double x, double y, double z) {
        double r8305122 = x;
        double r8305123 = y;
        double r8305124 = r8305122 + r8305123;
        double r8305125 = r8305124 + r8305123;
        double r8305126 = r8305125 + r8305122;
        double r8305127 = z;
        double r8305128 = r8305126 + r8305127;
        double r8305129 = r8305128 + r8305122;
        return r8305129;
}
↓
double f(double x, double y, double z) {
        double r8305130 = y;
        double r8305131 = r8305130 + r8305130;
        double r8305132 = 3.0;
        double r8305133 = x;
        double r8305134 = r8305132 * r8305133;
        double r8305135 = r8305131 + r8305134;
        double r8305136 = z;
        double r8305137 = r8305135 + r8305136;
        return r8305137;
}

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

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))