Average Error: 0.1 → 0.1
Time: 27.3s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(\left(\left(\left(y + z\right) + z\right) + y\right) \cdot x + t \cdot x\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(\left(\left(\left(y + z\right) + z\right) + y\right) \cdot x + t \cdot x\right) + y \cdot 5
double f(double x, double y, double z, double t) {
        double r141736 = x;
        double r141737 = y;
        double r141738 = z;
        double r141739 = r141737 + r141738;
        double r141740 = r141739 + r141738;
        double r141741 = r141740 + r141737;
        double r141742 = t;
        double r141743 = r141741 + r141742;
        double r141744 = r141736 * r141743;
        double r141745 = 5.0;
        double r141746 = r141737 * r141745;
        double r141747 = r141744 + r141746;
        return r141747;
}
↓
double f(double x, double y, double z, double t) {
        double r141748 = y;
        double r141749 = z;
        double r141750 = r141748 + r141749;
        double r141751 = r141750 + r141749;
        double r141752 = r141751 + r141748;
        double r141753 = x;
        double r141754 = r141752 * r141753;
        double r141755 = t;
        double r141756 = r141755 * r141753;
        double r141757 = r141754 + r141756;
        double r141758 = 5.0;
        double r141759 = r141748 * r141758;
        double r141760 = r141757 + r141759;
        return r141760;
}

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

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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)))