Average Error: 0.0 → 0.0
Time: 10.5s
Precision: 64
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[\frac{1 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]
\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
↓
\frac{1 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}
double f(double t) {
        double r1462981 = 1.0;
        double r1462982 = 2.0;
        double r1462983 = t;
        double r1462984 = r1462982 / r1462983;
        double r1462985 = r1462981 / r1462983;
        double r1462986 = r1462981 + r1462985;
        double r1462987 = r1462984 / r1462986;
        double r1462988 = r1462982 - r1462987;
        double r1462989 = r1462988 * r1462988;
        double r1462990 = r1462981 + r1462989;
        double r1462991 = r1462982 + r1462989;
        double r1462992 = r1462990 / r1462991;
        return r1462992;
}
↓
double f(double t) {
        double r1462993 = 1.0;
        double r1462994 = 2.0;
        double r1462995 = t;
        double r1462996 = r1462993 + r1462995;
        double r1462997 = r1462994 / r1462996;
        double r1462998 = r1462994 - r1462997;
        double r1462999 = r1462998 * r1462998;
        double r1463000 = r1462993 + r1462999;
        double r1463001 = r1462994 + r1462999;
        double r1463002 = r1463000 / r1463001;
        return r1463002;
}

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

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019152 
(FPCore (t)
  :name "Kahan p13 Example 2"
  (/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))))))