Average Error: 0.1 → 0.1
Time: 9.4s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[2 \cdot \left(x + y\right) + \left(x + z\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
2 \cdot \left(x + y\right) + \left(x + z\right)
double f(double x, double y, double z) {
        double r130551 = x;
        double r130552 = y;
        double r130553 = r130551 + r130552;
        double r130554 = r130553 + r130552;
        double r130555 = r130554 + r130551;
        double r130556 = z;
        double r130557 = r130555 + r130556;
        double r130558 = r130557 + r130551;
        return r130558;
}
↓
double f(double x, double y, double z) {
        double r130559 = 2.0;
        double r130560 = x;
        double r130561 = y;
        double r130562 = r130560 + r130561;
        double r130563 = r130559 * r130562;
        double r130564 = z;
        double r130565 = r130560 + r130564;
        double r130566 = r130563 + r130565;
        return r130566;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(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))