Average Error: 0.0 → 0.0
Time: 5.6s
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 r66840 = 1.0;
        double r66841 = 2.0;
        double r66842 = t;
        double r66843 = r66841 / r66842;
        double r66844 = r66840 / r66842;
        double r66845 = r66840 + r66844;
        double r66846 = r66843 / r66845;
        double r66847 = r66841 - r66846;
        double r66848 = r66847 * r66847;
        double r66849 = r66841 + r66848;
        double r66850 = r66840 / r66849;
        double r66851 = r66840 - r66850;
        return r66851;
}
↓
double f(double t) {
        double r66852 = 1.0;
        double r66853 = 2.0;
        double r66854 = t;
        double r66855 = r66853 / r66854;
        double r66856 = r66852 / r66854;
        double r66857 = r66852 + r66856;
        double r66858 = r66855 / r66857;
        double r66859 = r66853 - r66858;
        double r66860 = r66859 * r66859;
        double r66861 = r66853 + r66860;
        double r66862 = r66852 / r66861;
        double r66863 = r66852 - r66862;
        return r66863;
}

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 2020024 +o rules:numerics
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))