Average Error: 0.0 → 0.0
Time: 10.1s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
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(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
double f(double t) {
        double r49467 = 1.0;
        double r49468 = 2.0;
        double r49469 = t;
        double r49470 = r49468 / r49469;
        double r49471 = r49467 / r49469;
        double r49472 = r49467 + r49471;
        double r49473 = r49470 / r49472;
        double r49474 = r49468 - r49473;
        double r49475 = r49474 * r49474;
        double r49476 = r49468 + r49475;
        double r49477 = r49467 / r49476;
        double r49478 = r49467 - r49477;
        return r49478;
}
↓
double f(double t) {
        double r49479 = 1.0;
        double r49480 = 2.0;
        double r49481 = t;
        double r49482 = r49480 / r49481;
        double r49483 = r49479 / r49481;
        double r49484 = r49479 + r49483;
        double r49485 = r49482 / r49484;
        double r49486 = r49480 - r49485;
        double r49487 = r49486 * r49486;
        double r49488 = r49480 + r49487;
        double r49489 = r49479 / r49488;
        double r49490 = r49479 - r49489;
        return r49490;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019351 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))