Average Error: 0.0 → 0.0
Time: 3.2s
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 r44686 = 1.0;
        double r44687 = 2.0;
        double r44688 = t;
        double r44689 = r44687 / r44688;
        double r44690 = r44686 / r44688;
        double r44691 = r44686 + r44690;
        double r44692 = r44689 / r44691;
        double r44693 = r44687 - r44692;
        double r44694 = r44693 * r44693;
        double r44695 = r44687 + r44694;
        double r44696 = r44686 / r44695;
        double r44697 = r44686 - r44696;
        return r44697;
}
↓
double f(double t) {
        double r44698 = 1.0;
        double r44699 = 2.0;
        double r44700 = t;
        double r44701 = r44699 / r44700;
        double r44702 = r44698 / r44700;
        double r44703 = r44698 + r44702;
        double r44704 = r44701 / r44703;
        double r44705 = r44699 - r44704;
        double r44706 = r44705 * r44705;
        double r44707 = r44699 + r44706;
        double r44708 = r44698 / r44707;
        double r44709 = r44698 - r44708;
        return r44709;
}

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 +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)))))))))