Average Error: 0.1 → 0.1
Time: 37.7s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5.0\]
↓
\[\left(2 \cdot \left(x \cdot z\right) + \left(\left(x \cdot y\right) \cdot 2 + x \cdot t\right)\right) + y \cdot 5.0\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5.0
↓
\left(2 \cdot \left(x \cdot z\right) + \left(\left(x \cdot y\right) \cdot 2 + x \cdot t\right)\right) + y \cdot 5.0
double f(double x, double y, double z, double t) {
        double r8644886 = x;
        double r8644887 = y;
        double r8644888 = z;
        double r8644889 = r8644887 + r8644888;
        double r8644890 = r8644889 + r8644888;
        double r8644891 = r8644890 + r8644887;
        double r8644892 = t;
        double r8644893 = r8644891 + r8644892;
        double r8644894 = r8644886 * r8644893;
        double r8644895 = 5.0;
        double r8644896 = r8644887 * r8644895;
        double r8644897 = r8644894 + r8644896;
        return r8644897;
}
↓
double f(double x, double y, double z, double t) {
        double r8644898 = 2.0;
        double r8644899 = x;
        double r8644900 = z;
        double r8644901 = r8644899 * r8644900;
        double r8644902 = r8644898 * r8644901;
        double r8644903 = y;
        double r8644904 = r8644899 * r8644903;
        double r8644905 = r8644904 * r8644898;
        double r8644906 = t;
        double r8644907 = r8644899 * r8644906;
        double r8644908 = r8644905 + r8644907;
        double r8644909 = r8644902 + r8644908;
        double r8644910 = 5.0;
        double r8644911 = r8644903 * r8644910;
        double r8644912 = r8644909 + r8644911;
        return r8644912;
}

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

    \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5.0\]

  2. Simplified0.1

    \[\leadsto \color{blue}{y \cdot 5.0 + \left(\left(\left(y + z\right) + \left(y + z\right)\right) + t\right) \cdot x}\]

  3. Taylor expanded around inf 0.1

    \[\leadsto y \cdot 5.0 + \color{blue}{\left(2 \cdot \left(x \cdot z\right) + \left(t \cdot x + 2 \cdot \left(x \cdot y\right)\right)\right)}\]

  4. Final simplification0.1

    \[\leadsto \left(2 \cdot \left(x \cdot z\right) + \left(\left(x \cdot y\right) \cdot 2 + x \cdot t\right)\right) + y \cdot 5.0\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))