Average Error: 0.0 → 0.0
Time: 6.8s
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 r29603 = 1.0;
        double r29604 = 2.0;
        double r29605 = t;
        double r29606 = r29604 / r29605;
        double r29607 = r29603 / r29605;
        double r29608 = r29603 + r29607;
        double r29609 = r29606 / r29608;
        double r29610 = r29604 - r29609;
        double r29611 = r29610 * r29610;
        double r29612 = r29604 + r29611;
        double r29613 = r29603 / r29612;
        double r29614 = r29603 - r29613;
        return r29614;
}
↓
double f(double t) {
        double r29615 = 1.0;
        double r29616 = 2.0;
        double r29617 = t;
        double r29618 = r29616 / r29617;
        double r29619 = r29615 / r29617;
        double r29620 = r29615 + r29619;
        double r29621 = r29618 / r29620;
        double r29622 = r29616 - r29621;
        double r29623 = r29622 * r29622;
        double r29624 = r29616 + r29623;
        double r29625 = r29615 / r29624;
        double r29626 = r29615 - r29625;
        return r29626;
}

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 2020045 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))