Average Error: 0.0 → 0.0
Time: 6.8s
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 r27690 = 1.0;
        double r27691 = 2.0;
        double r27692 = t;
        double r27693 = r27691 / r27692;
        double r27694 = r27690 / r27692;
        double r27695 = r27690 + r27694;
        double r27696 = r27693 / r27695;
        double r27697 = r27691 - r27696;
        double r27698 = r27697 * r27697;
        double r27699 = r27690 + r27698;
        double r27700 = r27691 + r27698;
        double r27701 = r27699 / r27700;
        return r27701;
}
↓
double f(double t) {
        double r27702 = 1.0;
        double r27703 = 2.0;
        double r27704 = t;
        double r27705 = r27702 / r27704;
        double r27706 = r27705 + r27702;
        double r27707 = r27703 / r27706;
        double r27708 = r27707 / r27704;
        double r27709 = r27703 - r27708;
        double r27710 = r27709 * r27709;
        double r27711 = r27702 + r27710;
        double r27712 = r27703 + r27710;
        double r27713 = r27711 / r27712;
        return r27713;
}

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 2019196 
(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))))))))