Average Error: 0.1 → 0.1
Time: 8.0s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[x \cdot \left(\left(\left(y + z\right) + z\right) + y\right) + \left(t \cdot x + y \cdot 5\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
x \cdot \left(\left(\left(y + z\right) + z\right) + y\right) + \left(t \cdot x + y \cdot 5\right)
double f(double x, double y, double z, double t) {
        double r190777 = x;
        double r190778 = y;
        double r190779 = z;
        double r190780 = r190778 + r190779;
        double r190781 = r190780 + r190779;
        double r190782 = r190781 + r190778;
        double r190783 = t;
        double r190784 = r190782 + r190783;
        double r190785 = r190777 * r190784;
        double r190786 = 5.0;
        double r190787 = r190778 * r190786;
        double r190788 = r190785 + r190787;
        return r190788;
}
↓
double f(double x, double y, double z, double t) {
        double r190789 = x;
        double r190790 = y;
        double r190791 = z;
        double r190792 = r190790 + r190791;
        double r190793 = r190792 + r190791;
        double r190794 = r190793 + r190790;
        double r190795 = r190789 * r190794;
        double r190796 = t;
        double r190797 = r190796 * r190789;
        double r190798 = 5.0;
        double r190799 = r190790 * r190798;
        double r190800 = r190797 + r190799;
        double r190801 = r190795 + r190800;
        return r190801;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(x \cdot \left(\left(\left(y + z\right) + z\right) + y\right) + x \cdot t\right)} + y \cdot 5\]

  4. Applied associate-+l+0.1

    \[\leadsto \color{blue}{x \cdot \left(\left(\left(y + z\right) + z\right) + y\right) + \left(x \cdot t + y \cdot 5\right)}\]

  5. Simplified0.1

    \[\leadsto x \cdot \left(\left(\left(y + z\right) + z\right) + y\right) + \color{blue}{\left(t \cdot x + y \cdot 5\right)}\]

  6. Final simplification0.1

    \[\leadsto x \cdot \left(\left(\left(y + z\right) + z\right) + y\right) + \left(t \cdot x + y \cdot 5\right)\]

Reproduce

herbie shell --seed 2020039 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5)))