Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(\left(\sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}} \cdot \sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}}\right) \cdot \sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}}\right)}\]
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(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(\left(\sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}} \cdot \sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}}\right) \cdot \sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}}\right)}
double f(double t) {
        double r25624 = 1.0;
        double r25625 = 2.0;
        double r25626 = t;
        double r25627 = r25625 / r25626;
        double r25628 = r25624 / r25626;
        double r25629 = r25624 + r25628;
        double r25630 = r25627 / r25629;
        double r25631 = r25625 - r25630;
        double r25632 = r25631 * r25631;
        double r25633 = r25625 + r25632;
        double r25634 = r25624 / r25633;
        double r25635 = r25624 - r25634;
        return r25635;
}
↓
double f(double t) {
        double r25636 = 1.0;
        double r25637 = 2.0;
        double r25638 = t;
        double r25639 = r25637 / r25638;
        double r25640 = r25636 / r25638;
        double r25641 = r25636 + r25640;
        double r25642 = r25639 / r25641;
        double r25643 = r25637 - r25642;
        double r25644 = cbrt(r25643);
        double r25645 = r25644 * r25644;
        double r25646 = r25645 * r25644;
        double r25647 = r25643 * r25646;
        double r25648 = r25637 + r25647;
        double r25649 = r25636 / r25648;
        double r25650 = r25636 - r25649;
        return r25650;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))