Average Error: 0.1 → 0.1
Time: 11.0s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[x \cdot \left(\left(\left(y + \left(z + z\right)\right) + y\right) + t\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
x \cdot \left(\left(\left(y + \left(z + z\right)\right) + y\right) + t\right) + y \cdot 5
double f(double x, double y, double z, double t) {
        double r193896 = x;
        double r193897 = y;
        double r193898 = z;
        double r193899 = r193897 + r193898;
        double r193900 = r193899 + r193898;
        double r193901 = r193900 + r193897;
        double r193902 = t;
        double r193903 = r193901 + r193902;
        double r193904 = r193896 * r193903;
        double r193905 = 5.0;
        double r193906 = r193897 * r193905;
        double r193907 = r193904 + r193906;
        return r193907;
}
↓
double f(double x, double y, double z, double t) {
        double r193908 = x;
        double r193909 = y;
        double r193910 = z;
        double r193911 = r193910 + r193910;
        double r193912 = r193909 + r193911;
        double r193913 = r193912 + r193909;
        double r193914 = t;
        double r193915 = r193913 + r193914;
        double r193916 = r193908 * r193915;
        double r193917 = 5.0;
        double r193918 = r193909 * r193917;
        double r193919 = r193916 + r193918;
        return r193919;
}

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 associate-+l+0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020002 
(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)))