Average Error: 0.1 → 0.1
Time: 13.9s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[z + \left(x \cdot 3 + \left(y + y\right)\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
z + \left(x \cdot 3 + \left(y + y\right)\right)
double f(double x, double y, double z) {
        double r163962 = x;
        double r163963 = y;
        double r163964 = r163962 + r163963;
        double r163965 = r163964 + r163963;
        double r163966 = r163965 + r163962;
        double r163967 = z;
        double r163968 = r163966 + r163967;
        double r163969 = r163968 + r163962;
        return r163969;
}
↓
double f(double x, double y, double z) {
        double r163970 = z;
        double r163971 = x;
        double r163972 = 3.0;
        double r163973 = r163971 * r163972;
        double r163974 = y;
        double r163975 = r163974 + r163974;
        double r163976 = r163973 + r163975;
        double r163977 = r163970 + r163976;
        return r163977;
}

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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))