Average Error: 0.0 → 0.0
Time: 6.4s
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 r570372 = 1.0;
        double r570373 = 2.0;
        double r570374 = t;
        double r570375 = r570373 / r570374;
        double r570376 = r570372 / r570374;
        double r570377 = r570372 + r570376;
        double r570378 = r570375 / r570377;
        double r570379 = r570373 - r570378;
        double r570380 = r570379 * r570379;
        double r570381 = r570373 + r570380;
        double r570382 = r570372 / r570381;
        double r570383 = r570372 - r570382;
        return r570383;
}
↓
double f(double t) {
        double r570384 = 1.0;
        double r570385 = 2.0;
        double r570386 = t;
        double r570387 = r570384 + r570386;
        double r570388 = r570385 / r570387;
        double r570389 = r570385 - r570388;
        double r570390 = r570389 * r570389;
        double r570391 = r570385 + r570390;
        double r570392 = r570384 / r570391;
        double r570393 = r570384 - r570392;
        return r570393;
}

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 2019152 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))