Average Error: 0.0 → 0.0
Time: 7.3s
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 r26345 = 1.0;
        double r26346 = 2.0;
        double r26347 = t;
        double r26348 = r26346 / r26347;
        double r26349 = r26345 / r26347;
        double r26350 = r26345 + r26349;
        double r26351 = r26348 / r26350;
        double r26352 = r26346 - r26351;
        double r26353 = r26352 * r26352;
        double r26354 = r26346 + r26353;
        double r26355 = r26345 / r26354;
        double r26356 = r26345 - r26355;
        return r26356;
}
↓
double f(double t) {
        double r26357 = 1.0;
        double r26358 = 2.0;
        double r26359 = t;
        double r26360 = r26358 / r26359;
        double r26361 = r26357 / r26359;
        double r26362 = r26357 + r26361;
        double r26363 = r26360 / r26362;
        double r26364 = r26358 - r26363;
        double r26365 = r26364 * r26364;
        double r26366 = r26358 + r26365;
        double r26367 = r26357 / r26366;
        double r26368 = r26357 - r26367;
        return r26368;
}

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 2020043 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))