Average Error: 0.0 → 0.0
Time: 16.7s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\left(\left(\sqrt[3]{2 - \frac{2}{1 \cdot t + 1}} \cdot \sqrt[3]{2 - \frac{2}{1 \cdot t + 1}}\right) \cdot \sqrt[3]{2 - \frac{2}{1 \cdot t + 1}}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right) + 2}\]
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}{\left(\left(\sqrt[3]{2 - \frac{2}{1 \cdot t + 1}} \cdot \sqrt[3]{2 - \frac{2}{1 \cdot t + 1}}\right) \cdot \sqrt[3]{2 - \frac{2}{1 \cdot t + 1}}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right) + 2}
double f(double t) {
        double r2141527 = 1.0;
        double r2141528 = 2.0;
        double r2141529 = t;
        double r2141530 = r2141528 / r2141529;
        double r2141531 = r2141527 / r2141529;
        double r2141532 = r2141527 + r2141531;
        double r2141533 = r2141530 / r2141532;
        double r2141534 = r2141528 - r2141533;
        double r2141535 = r2141534 * r2141534;
        double r2141536 = r2141528 + r2141535;
        double r2141537 = r2141527 / r2141536;
        double r2141538 = r2141527 - r2141537;
        return r2141538;
}
↓
double f(double t) {
        double r2141539 = 1.0;
        double r2141540 = 2.0;
        double r2141541 = t;
        double r2141542 = r2141539 * r2141541;
        double r2141543 = r2141542 + r2141539;
        double r2141544 = r2141540 / r2141543;
        double r2141545 = r2141540 - r2141544;
        double r2141546 = cbrt(r2141545);
        double r2141547 = r2141546 * r2141546;
        double r2141548 = r2141547 * r2141546;
        double r2141549 = r2141548 * r2141545;
        double r2141550 = r2141549 + r2141540;
        double r2141551 = r2141539 / r2141550;
        double r2141552 = r2141539 - r2141551;
        return r2141552;
}

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

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

  4. Applied add-cube-cbrt0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1.0 (/ 1.0 (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))))))