Average Error: 0.1 → 0.1
Time: 17.6s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(\left(y + y\right) + z\right) + 3 \cdot x\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(\left(y + y\right) + z\right) + 3 \cdot x
double f(double x, double y, double z) {
        double r8974449 = x;
        double r8974450 = y;
        double r8974451 = r8974449 + r8974450;
        double r8974452 = r8974451 + r8974450;
        double r8974453 = r8974452 + r8974449;
        double r8974454 = z;
        double r8974455 = r8974453 + r8974454;
        double r8974456 = r8974455 + r8974449;
        return r8974456;
}
↓
double f(double x, double y, double z) {
        double r8974457 = y;
        double r8974458 = r8974457 + r8974457;
        double r8974459 = z;
        double r8974460 = r8974458 + r8974459;
        double r8974461 = 3.0;
        double r8974462 = x;
        double r8974463 = r8974461 * r8974462;
        double r8974464 = r8974460 + r8974463;
        return r8974464;
}

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

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))