Average Error: 0.1 → 0.1
Time: 5.9s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(2 \cdot \left(z + y\right) + t\right) \cdot x + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(2 \cdot \left(z + y\right) + t\right) \cdot x + y \cdot 5
double f(double x, double y, double z, double t) {
        double r167870 = x;
        double r167871 = y;
        double r167872 = z;
        double r167873 = r167871 + r167872;
        double r167874 = r167873 + r167872;
        double r167875 = r167874 + r167871;
        double r167876 = t;
        double r167877 = r167875 + r167876;
        double r167878 = r167870 * r167877;
        double r167879 = 5.0;
        double r167880 = r167871 * r167879;
        double r167881 = r167878 + r167880;
        return r167881;
}
↓
double f(double x, double y, double z, double t) {
        double r167882 = 2.0;
        double r167883 = z;
        double r167884 = y;
        double r167885 = r167883 + r167884;
        double r167886 = r167882 * r167885;
        double r167887 = t;
        double r167888 = r167886 + r167887;
        double r167889 = x;
        double r167890 = r167888 * r167889;
        double r167891 = 5.0;
        double r167892 = r167884 * r167891;
        double r167893 = r167890 + r167892;
        return r167893;
}

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. Taylor expanded around inf 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020081 
(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)))