Average Error: 0.1 → 0.1
Time: 15.8s
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 r105798 = x;
        double r105799 = y;
        double r105800 = r105798 + r105799;
        double r105801 = r105800 + r105799;
        double r105802 = r105801 + r105798;
        double r105803 = z;
        double r105804 = r105802 + r105803;
        double r105805 = r105804 + r105798;
        return r105805;
}
↓
double f(double x, double y, double z) {
        double r105806 = 3.0;
        double r105807 = x;
        double r105808 = r105806 * r105807;
        double r105809 = z;
        double r105810 = 2.0;
        double r105811 = y;
        double r105812 = r105810 * r105811;
        double r105813 = r105809 + r105812;
        double r105814 = r105808 + r105813;
        return r105814;
}

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

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

  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 2019198 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))