Average Error: 0.0 → 0.0
Time: 1.3s
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 r48383 = 1.0;
        double r48384 = 2.0;
        double r48385 = t;
        double r48386 = r48384 / r48385;
        double r48387 = r48383 / r48385;
        double r48388 = r48383 + r48387;
        double r48389 = r48386 / r48388;
        double r48390 = r48384 - r48389;
        double r48391 = r48390 * r48390;
        double r48392 = r48384 + r48391;
        double r48393 = r48383 / r48392;
        double r48394 = r48383 - r48393;
        return r48394;
}
↓
double f(double t) {
        double r48395 = 1.0;
        double r48396 = 2.0;
        double r48397 = t;
        double r48398 = r48396 / r48397;
        double r48399 = r48395 / r48397;
        double r48400 = r48395 + r48399;
        double r48401 = r48398 / r48400;
        double r48402 = r48396 - r48401;
        double r48403 = r48402 * r48402;
        double r48404 = r48396 + r48403;
        double r48405 = r48395 / r48404;
        double r48406 = r48395 - r48405;
        return r48406;
}

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 2020065 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))