Average Error: 0.0 → 0.0
Time: 9.9s
Precision: 64
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[\frac{1 + \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right) \cdot \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right)}{2 + \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right) \cdot \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right)}\]
\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{\frac{2}{\frac{1}{t} + 1}}{t}\right) \cdot \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right)}{2 + \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right) \cdot \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right)}
double f(double t) {
        double r34795 = 1.0;
        double r34796 = 2.0;
        double r34797 = t;
        double r34798 = r34796 / r34797;
        double r34799 = r34795 / r34797;
        double r34800 = r34795 + r34799;
        double r34801 = r34798 / r34800;
        double r34802 = r34796 - r34801;
        double r34803 = r34802 * r34802;
        double r34804 = r34795 + r34803;
        double r34805 = r34796 + r34803;
        double r34806 = r34804 / r34805;
        return r34806;
}
↓
double f(double t) {
        double r34807 = 1.0;
        double r34808 = 2.0;
        double r34809 = t;
        double r34810 = r34807 / r34809;
        double r34811 = r34810 + r34807;
        double r34812 = r34808 / r34811;
        double r34813 = r34812 / r34809;
        double r34814 = r34808 - r34813;
        double r34815 = r34814 * r34814;
        double r34816 = r34807 + r34815;
        double r34817 = r34808 + r34815;
        double r34818 = r34816 / r34817;
        return r34818;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(FPCore (t)
  :name "Kahan p13 Example 2"
  (/ (+ 1.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))) (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))))))