Average Error: 0.1 → 0.1
Time: 1.9s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[x \cdot 2 + \left(y \cdot 2 + \left(x + z\right)\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
x \cdot 2 + \left(y \cdot 2 + \left(x + z\right)\right)
double f(double x, double y, double z) {
        double r173536 = x;
        double r173537 = y;
        double r173538 = r173536 + r173537;
        double r173539 = r173538 + r173537;
        double r173540 = r173539 + r173536;
        double r173541 = z;
        double r173542 = r173540 + r173541;
        double r173543 = r173542 + r173536;
        return r173543;
}
↓
double f(double x, double y, double z) {
        double r173544 = x;
        double r173545 = 2.0;
        double r173546 = r173544 * r173545;
        double r173547 = y;
        double r173548 = r173547 * r173545;
        double r173549 = z;
        double r173550 = r173544 + r173549;
        double r173551 = r173548 + r173550;
        double r173552 = r173546 + r173551;
        return r173552;
}

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. Using strategy rm

  4. Applied distribute-rgt-in0.1

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

  5. Applied associate-+l+0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(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))