Average Error: 0.0 → 0.0
Time: 2.9s
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 r57440 = 1.0;
        double r57441 = 2.0;
        double r57442 = t;
        double r57443 = r57441 / r57442;
        double r57444 = r57440 / r57442;
        double r57445 = r57440 + r57444;
        double r57446 = r57443 / r57445;
        double r57447 = r57441 - r57446;
        double r57448 = r57447 * r57447;
        double r57449 = r57441 + r57448;
        double r57450 = r57440 / r57449;
        double r57451 = r57440 - r57450;
        return r57451;
}
↓
double f(double t) {
        double r57452 = 1.0;
        double r57453 = 2.0;
        double r57454 = t;
        double r57455 = r57453 / r57454;
        double r57456 = r57452 / r57454;
        double r57457 = r57452 + r57456;
        double r57458 = r57455 / r57457;
        double r57459 = r57453 - r57458;
        double r57460 = r57459 * r57459;
        double r57461 = r57453 + r57460;
        double r57462 = r57452 / r57461;
        double r57463 = r57452 - r57462;
        return r57463;
}

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 +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)))))))))