Average Error: 0.0 → 0.0
Time: 5.7s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]
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{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}
double f(double t) {
        double r575361 = 1.0;
        double r575362 = 2.0;
        double r575363 = t;
        double r575364 = r575362 / r575363;
        double r575365 = r575361 / r575363;
        double r575366 = r575361 + r575365;
        double r575367 = r575364 / r575366;
        double r575368 = r575362 - r575367;
        double r575369 = r575368 * r575368;
        double r575370 = r575362 + r575369;
        double r575371 = r575361 / r575370;
        double r575372 = r575361 - r575371;
        return r575372;
}
↓
double f(double t) {
        double r575373 = 1.0;
        double r575374 = 2.0;
        double r575375 = t;
        double r575376 = r575373 + r575375;
        double r575377 = r575374 / r575376;
        double r575378 = r575374 - r575377;
        double r575379 = r575378 * r575378;
        double r575380 = r575374 + r575379;
        double r575381 = r575373 / r575380;
        double r575382 = r575373 - r575381;
        return r575382;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019154 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))