Average Error: 0.1 → 0.1
Time: 14.1s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[3 \cdot x + \left(z + 2 \cdot y\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
3 \cdot x + \left(z + 2 \cdot y\right)
double f(double x, double y, double z) {
        double r108941 = x;
        double r108942 = y;
        double r108943 = r108941 + r108942;
        double r108944 = r108943 + r108942;
        double r108945 = r108944 + r108941;
        double r108946 = z;
        double r108947 = r108945 + r108946;
        double r108948 = r108947 + r108941;
        return r108948;
}
↓
double f(double x, double y, double z) {
        double r108949 = 3.0;
        double r108950 = x;
        double r108951 = r108949 * r108950;
        double r108952 = z;
        double r108953 = 2.0;
        double r108954 = y;
        double r108955 = r108953 * r108954;
        double r108956 = r108952 + r108955;
        double r108957 = r108951 + r108956;
        return r108957;
}

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

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

  3. Taylor expanded around 0 0.1

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

  4. Final simplification0.1

    \[\leadsto 3 \cdot x + \left(z + 2 \cdot y\right)\]

Reproduce

herbie shell --seed 2019294 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  :precision binary64
  (+ (+ (+ (+ (+ x y) y) x) z) x))