Average Error: 0.1 → 0.1
Time: 20.8s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[x \cdot 3 + \left(z + \left(y + y\right)\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
x \cdot 3 + \left(z + \left(y + y\right)\right)
double f(double x, double y, double z) {
        double r8451044 = x;
        double r8451045 = y;
        double r8451046 = r8451044 + r8451045;
        double r8451047 = r8451046 + r8451045;
        double r8451048 = r8451047 + r8451044;
        double r8451049 = z;
        double r8451050 = r8451048 + r8451049;
        double r8451051 = r8451050 + r8451044;
        return r8451051;
}
↓
double f(double x, double y, double z) {
        double r8451052 = x;
        double r8451053 = 3.0;
        double r8451054 = r8451052 * r8451053;
        double r8451055 = z;
        double r8451056 = y;
        double r8451057 = r8451056 + r8451056;
        double r8451058 = r8451055 + r8451057;
        double r8451059 = r8451054 + r8451058;
        return r8451059;
}

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. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))