Average Error: 0.1 → 0.1
Time: 4.4s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(\left(2 \cdot \left(x \cdot y\right) + 2 \cdot \left(x \cdot z\right)\right) + x \cdot t\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(\left(2 \cdot \left(x \cdot y\right) + 2 \cdot \left(x \cdot z\right)\right) + x \cdot t\right) + y \cdot 5
double f(double x, double y, double z, double t) {
        double r171896 = x;
        double r171897 = y;
        double r171898 = z;
        double r171899 = r171897 + r171898;
        double r171900 = r171899 + r171898;
        double r171901 = r171900 + r171897;
        double r171902 = t;
        double r171903 = r171901 + r171902;
        double r171904 = r171896 * r171903;
        double r171905 = 5.0;
        double r171906 = r171897 * r171905;
        double r171907 = r171904 + r171906;
        return r171907;
}
↓
double f(double x, double y, double z, double t) {
        double r171908 = 2.0;
        double r171909 = x;
        double r171910 = y;
        double r171911 = r171909 * r171910;
        double r171912 = r171908 * r171911;
        double r171913 = z;
        double r171914 = r171909 * r171913;
        double r171915 = r171908 * r171914;
        double r171916 = r171912 + r171915;
        double r171917 = t;
        double r171918 = r171909 * r171917;
        double r171919 = r171916 + r171918;
        double r171920 = 5.0;
        double r171921 = r171910 * r171920;
        double r171922 = r171919 + r171921;
        return r171922;
}

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. Using strategy rm

  6. Applied distribute-lft-in0.1

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

  7. Simplified0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 
(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)))