Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
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 r42344 = 1.0;
        double r42345 = 2.0;
        double r42346 = t;
        double r42347 = r42345 / r42346;
        double r42348 = r42344 / r42346;
        double r42349 = r42344 + r42348;
        double r42350 = r42347 / r42349;
        double r42351 = r42345 - r42350;
        double r42352 = r42351 * r42351;
        double r42353 = r42345 + r42352;
        double r42354 = r42344 / r42353;
        double r42355 = r42344 - r42354;
        return r42355;
}
↓
double f(double t) {
        double r42356 = 1.0;
        double r42357 = 2.0;
        double r42358 = t;
        double r42359 = r42357 / r42358;
        double r42360 = r42356 / r42358;
        double r42361 = r42356 + r42360;
        double r42362 = r42359 / r42361;
        double r42363 = r42357 - r42362;
        double r42364 = r42363 * r42363;
        double r42365 = r42357 + r42364;
        double r42366 = r42356 / r42365;
        double r42367 = r42356 - r42366;
        return r42367;
}

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 2020060 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))