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 r34632 = 1.0;
        double r34633 = 2.0;
        double r34634 = t;
        double r34635 = r34633 / r34634;
        double r34636 = r34632 / r34634;
        double r34637 = r34632 + r34636;
        double r34638 = r34635 / r34637;
        double r34639 = r34633 - r34638;
        double r34640 = r34639 * r34639;
        double r34641 = r34633 + r34640;
        double r34642 = r34632 / r34641;
        double r34643 = r34632 - r34642;
        return r34643;
}
↓
double f(double t) {
        double r34644 = 1.0;
        double r34645 = 2.0;
        double r34646 = t;
        double r34647 = r34645 / r34646;
        double r34648 = r34644 / r34646;
        double r34649 = r34644 + r34648;
        double r34650 = r34647 / r34649;
        double r34651 = r34645 - r34650;
        double r34652 = r34651 * r34651;
        double r34653 = r34645 + r34652;
        double r34654 = r34644 / r34653;
        double r34655 = r34644 - r34654;
        return r34655;
}

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 2020002 +o rules:numerics
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))