Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]
1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
↓
1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}
double f(double t) {
        double r482910 = 1.0;
        double r482911 = 2.0;
        double r482912 = t;
        double r482913 = r482911 / r482912;
        double r482914 = r482910 / r482912;
        double r482915 = r482910 + r482914;
        double r482916 = r482913 / r482915;
        double r482917 = r482911 - r482916;
        double r482918 = r482917 * r482917;
        double r482919 = r482911 + r482918;
        double r482920 = r482910 / r482919;
        double r482921 = r482910 - r482920;
        return r482921;
}
↓
double f(double t) {
        double r482922 = 1.0;
        double r482923 = 2.0;
        double r482924 = t;
        double r482925 = r482922 + r482924;
        double r482926 = r482923 / r482925;
        double r482927 = r482923 - r482926;
        double r482928 = r482927 * r482927;
        double r482929 = r482923 + r482928;
        double r482930 = r482922 / r482929;
        double r482931 = r482922 - r482930;
        return r482931;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}}\]

  3. Final simplification0.0

    \[\leadsto 1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]

Reproduce

herbie shell --seed 2019142 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))