Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(\sqrt[3]{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)} \cdot \sqrt[3]{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\right) \cdot \sqrt[3]{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}}\]
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(\sqrt[3]{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)} \cdot \sqrt[3]{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\right) \cdot \sqrt[3]{\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 r35436 = 1.0;
        double r35437 = 2.0;
        double r35438 = t;
        double r35439 = r35437 / r35438;
        double r35440 = r35436 / r35438;
        double r35441 = r35436 + r35440;
        double r35442 = r35439 / r35441;
        double r35443 = r35437 - r35442;
        double r35444 = r35443 * r35443;
        double r35445 = r35437 + r35444;
        double r35446 = r35436 / r35445;
        double r35447 = r35436 - r35446;
        return r35447;
}
↓
double f(double t) {
        double r35448 = 1.0;
        double r35449 = 2.0;
        double r35450 = t;
        double r35451 = r35449 / r35450;
        double r35452 = r35448 / r35450;
        double r35453 = r35448 + r35452;
        double r35454 = r35451 / r35453;
        double r35455 = r35449 - r35454;
        double r35456 = r35455 * r35455;
        double r35457 = cbrt(r35456);
        double r35458 = r35457 * r35457;
        double r35459 = r35458 * r35457;
        double r35460 = r35449 + r35459;
        double r35461 = r35448 / r35460;
        double r35462 = r35448 - r35461;
        return r35462;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.0

    \[\leadsto 1 - \frac{1}{2 + \color{blue}{\left(\sqrt[3]{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)} \cdot \sqrt[3]{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\right) \cdot \sqrt[3]{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}}}\]

  4. Final simplification0.0

    \[\leadsto 1 - \frac{1}{2 + \left(\sqrt[3]{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)} \cdot \sqrt[3]{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\right) \cdot \sqrt[3]{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}}\]

Reproduce

herbie shell --seed 2020025 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))