Average Error: 0.1 → 0.1
Time: 8.4s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(\left(2 \cdot x\right) \cdot \left(y + z\right) + x \cdot t\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(\left(2 \cdot x\right) \cdot \left(y + z\right) + x \cdot t\right) + y \cdot 5
double f(double x, double y, double z, double t) {
        double r181689 = x;
        double r181690 = y;
        double r181691 = z;
        double r181692 = r181690 + r181691;
        double r181693 = r181692 + r181691;
        double r181694 = r181693 + r181690;
        double r181695 = t;
        double r181696 = r181694 + r181695;
        double r181697 = r181689 * r181696;
        double r181698 = 5.0;
        double r181699 = r181690 * r181698;
        double r181700 = r181697 + r181699;
        return r181700;
}
↓
double f(double x, double y, double z, double t) {
        double r181701 = 2.0;
        double r181702 = x;
        double r181703 = r181701 * r181702;
        double r181704 = y;
        double r181705 = z;
        double r181706 = r181704 + r181705;
        double r181707 = r181703 * r181706;
        double r181708 = t;
        double r181709 = r181702 * r181708;
        double r181710 = r181707 + r181709;
        double r181711 = 5.0;
        double r181712 = r181704 * r181711;
        double r181713 = r181710 + r181712;
        return r181713;
}

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. Simplified0.1

    \[\leadsto \left(\color{blue}{\left(2 \cdot x\right) \cdot \left(y + z\right)} + x \cdot t\right) + y \cdot 5\]

  5. Final simplification0.1

    \[\leadsto \left(\left(2 \cdot x\right) \cdot \left(y + z\right) + x \cdot t\right) + y \cdot 5\]

Reproduce

herbie shell --seed 2020035 
(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)))