Average Error: 0.0 → 0.0
Time: 7.1s
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 r27487 = 1.0;
        double r27488 = 2.0;
        double r27489 = t;
        double r27490 = r27488 / r27489;
        double r27491 = r27487 / r27489;
        double r27492 = r27487 + r27491;
        double r27493 = r27490 / r27492;
        double r27494 = r27488 - r27493;
        double r27495 = r27494 * r27494;
        double r27496 = r27488 + r27495;
        double r27497 = r27487 / r27496;
        double r27498 = r27487 - r27497;
        return r27498;
}
↓
double f(double t) {
        double r27499 = 1.0;
        double r27500 = 2.0;
        double r27501 = t;
        double r27502 = r27500 / r27501;
        double r27503 = r27499 / r27501;
        double r27504 = r27499 + r27503;
        double r27505 = r27502 / r27504;
        double r27506 = r27500 - r27505;
        double r27507 = r27506 * r27506;
        double r27508 = r27500 + r27507;
        double r27509 = r27499 / r27508;
        double r27510 = r27499 - r27509;
        return r27510;
}

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 2019297 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))