Average Error: 0.0 → 0.0
Time: 9.1s
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 r1107908 = 1.0;
        double r1107909 = 2.0;
        double r1107910 = t;
        double r1107911 = r1107909 / r1107910;
        double r1107912 = r1107908 / r1107910;
        double r1107913 = r1107908 + r1107912;
        double r1107914 = r1107911 / r1107913;
        double r1107915 = r1107909 - r1107914;
        double r1107916 = r1107915 * r1107915;
        double r1107917 = r1107909 + r1107916;
        double r1107918 = r1107908 / r1107917;
        double r1107919 = r1107908 - r1107918;
        return r1107919;
}
↓
double f(double t) {
        double r1107920 = 1.0;
        double r1107921 = 2.0;
        double r1107922 = t;
        double r1107923 = r1107920 + r1107922;
        double r1107924 = r1107921 / r1107923;
        double r1107925 = r1107921 - r1107924;
        double r1107926 = r1107925 * r1107925;
        double r1107927 = r1107921 + r1107926;
        double r1107928 = r1107920 / r1107927;
        double r1107929 = r1107920 - r1107928;
        return r1107929;
}

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 2019152 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))