Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
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 r27385 = 1.0;
        double r27386 = 2.0;
        double r27387 = t;
        double r27388 = r27386 / r27387;
        double r27389 = r27385 / r27387;
        double r27390 = r27385 + r27389;
        double r27391 = r27388 / r27390;
        double r27392 = r27386 - r27391;
        double r27393 = r27392 * r27392;
        double r27394 = r27386 + r27393;
        double r27395 = r27385 / r27394;
        double r27396 = r27385 - r27395;
        return r27396;
}
↓
double f(double t) {
        double r27397 = 1.0;
        double r27398 = 2.0;
        double r27399 = t;
        double r27400 = r27398 / r27399;
        double r27401 = r27397 / r27399;
        double r27402 = r27397 + r27401;
        double r27403 = r27400 / r27402;
        double r27404 = r27398 - r27403;
        double r27405 = r27404 * r27404;
        double r27406 = r27398 + r27405;
        double r27407 = r27397 / r27406;
        double r27408 = r27397 - r27407;
        return r27408;
}

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 2020056 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))