Average Error: 0.0 → 0.0
Time: 2.5s
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 r38657 = 1.0;
        double r38658 = 2.0;
        double r38659 = t;
        double r38660 = r38658 / r38659;
        double r38661 = r38657 / r38659;
        double r38662 = r38657 + r38661;
        double r38663 = r38660 / r38662;
        double r38664 = r38658 - r38663;
        double r38665 = r38664 * r38664;
        double r38666 = r38658 + r38665;
        double r38667 = r38657 / r38666;
        double r38668 = r38657 - r38667;
        return r38668;
}
↓
double f(double t) {
        double r38669 = 1.0;
        double r38670 = 2.0;
        double r38671 = t;
        double r38672 = r38670 / r38671;
        double r38673 = r38669 / r38671;
        double r38674 = r38669 + r38673;
        double r38675 = r38672 / r38674;
        double r38676 = r38670 - r38675;
        double r38677 = r38676 * r38676;
        double r38678 = r38670 + r38677;
        double r38679 = r38669 / r38678;
        double r38680 = r38669 - r38679;
        return r38680;
}

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 2020039 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))