Average Error: 0.0 → 0.0
Time: 7.4s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right) + 2}\]
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(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right) + 2}
double f(double t) {
        double r1371430 = 1.0;
        double r1371431 = 2.0;
        double r1371432 = t;
        double r1371433 = r1371431 / r1371432;
        double r1371434 = r1371430 / r1371432;
        double r1371435 = r1371430 + r1371434;
        double r1371436 = r1371433 / r1371435;
        double r1371437 = r1371431 - r1371436;
        double r1371438 = r1371437 * r1371437;
        double r1371439 = r1371431 + r1371438;
        double r1371440 = r1371430 / r1371439;
        double r1371441 = r1371430 - r1371440;
        return r1371441;
}
↓
double f(double t) {
        double r1371442 = 1.0;
        double r1371443 = 2.0;
        double r1371444 = t;
        double r1371445 = r1371442 * r1371444;
        double r1371446 = r1371445 + r1371442;
        double r1371447 = r1371443 / r1371446;
        double r1371448 = r1371443 - r1371447;
        double r1371449 = r1371448 * r1371448;
        double r1371450 = r1371449 + r1371443;
        double r1371451 = r1371442 / r1371450;
        double r1371452 = r1371442 - r1371451;
        return r1371452;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(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)))))))))