Average Error: 0.0 → 0.0
Time: 5.2s
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 r69398 = 1.0;
        double r69399 = 2.0;
        double r69400 = t;
        double r69401 = r69399 / r69400;
        double r69402 = r69398 / r69400;
        double r69403 = r69398 + r69402;
        double r69404 = r69401 / r69403;
        double r69405 = r69399 - r69404;
        double r69406 = r69405 * r69405;
        double r69407 = r69399 + r69406;
        double r69408 = r69398 / r69407;
        double r69409 = r69398 - r69408;
        return r69409;
}
↓
double f(double t) {
        double r69410 = 1.0;
        double r69411 = 2.0;
        double r69412 = t;
        double r69413 = r69411 / r69412;
        double r69414 = r69410 / r69412;
        double r69415 = r69410 + r69414;
        double r69416 = r69413 / r69415;
        double r69417 = r69411 - r69416;
        double r69418 = r69417 * r69417;
        double r69419 = r69411 + r69418;
        double r69420 = r69410 / r69419;
        double r69421 = r69410 - r69420;
        return r69421;
}

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)))))))))