Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
1 - \frac{1}{2 + \left(2 - \frac{\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{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
double f(double t) {
        double r32882 = 1.0;
        double r32883 = 2.0;
        double r32884 = t;
        double r32885 = r32883 / r32884;
        double r32886 = r32882 / r32884;
        double r32887 = r32882 + r32886;
        double r32888 = r32885 / r32887;
        double r32889 = r32883 - r32888;
        double r32890 = r32889 * r32889;
        double r32891 = r32883 + r32890;
        double r32892 = r32882 / r32891;
        double r32893 = r32882 - r32892;
        return r32893;
}
↓
double f(double t) {
        double r32894 = 1.0;
        double r32895 = 2.0;
        double r32896 = t;
        double r32897 = r32895 / r32896;
        double r32898 = r32894 / r32896;
        double r32899 = r32894 + r32898;
        double r32900 = r32897 / r32899;
        double r32901 = r32895 - r32900;
        double r32902 = r32901 * r32901;
        double r32903 = r32895 + r32902;
        double r32904 = r32894 / r32903;
        double r32905 = r32894 - r32904;
        return r32905;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020020 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))