Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right) + 2}\]
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}{\left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right) + 2}
double f(double t) {
        double r28350 = 1.0;
        double r28351 = 2.0;
        double r28352 = t;
        double r28353 = r28351 / r28352;
        double r28354 = r28350 / r28352;
        double r28355 = r28350 + r28354;
        double r28356 = r28353 / r28355;
        double r28357 = r28351 - r28356;
        double r28358 = r28357 * r28357;
        double r28359 = r28351 + r28358;
        double r28360 = r28350 / r28359;
        double r28361 = r28350 - r28360;
        return r28361;
}
↓
double f(double t) {
        double r28362 = 1.0;
        double r28363 = 2.0;
        double r28364 = t;
        double r28365 = r28362 * r28364;
        double r28366 = r28365 + r28362;
        double r28367 = r28363 / r28366;
        double r28368 = r28363 - r28367;
        double r28369 = r28368 * r28368;
        double r28370 = r28369 + r28363;
        double r28371 = r28362 / r28370;
        double r28372 = r28362 - r28371;
        return r28372;
}

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. Simplified0.0

    \[\leadsto \color{blue}{1 - \frac{1}{2 + \left(2 - \frac{2}{1 + 1 \cdot t}\right) \cdot \left(2 - \frac{2}{1 + 1 \cdot t}\right)}}\]

  3. Final simplification0.0

    \[\leadsto 1 - \frac{1}{\left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right) + 2}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1.0 (/ 1.0 (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))))))