Average Error: 0.0 → 0.0
Time: 6.9s
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 r1393338 = 1.0;
        double r1393339 = 2.0;
        double r1393340 = t;
        double r1393341 = r1393339 / r1393340;
        double r1393342 = r1393338 / r1393340;
        double r1393343 = r1393338 + r1393342;
        double r1393344 = r1393341 / r1393343;
        double r1393345 = r1393339 - r1393344;
        double r1393346 = r1393345 * r1393345;
        double r1393347 = r1393339 + r1393346;
        double r1393348 = r1393338 / r1393347;
        double r1393349 = r1393338 - r1393348;
        return r1393349;
}
↓
double f(double t) {
        double r1393350 = 1.0;
        double r1393351 = 2.0;
        double r1393352 = t;
        double r1393353 = r1393350 * r1393352;
        double r1393354 = r1393353 + r1393350;
        double r1393355 = r1393351 / r1393354;
        double r1393356 = r1393351 - r1393355;
        double r1393357 = r1393356 * r1393356;
        double r1393358 = r1393357 + r1393351;
        double r1393359 = r1393350 / r1393358;
        double r1393360 = r1393350 - r1393359;
        return r1393360;
}

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 2019172 
(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)))))))))