Average Error: 0.0 → 0.0
Time: 8.3s
Precision: 64
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[\frac{1 + \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right) \cdot \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right)}{2 + \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right) \cdot \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right)}\]
\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
↓
\frac{1 + \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right) \cdot \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right)}{2 + \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right) \cdot \left(2 - \frac{\frac{2}{\frac{1}{t} + 1}}{t}\right)}
double f(double t) {
        double r32380 = 1.0;
        double r32381 = 2.0;
        double r32382 = t;
        double r32383 = r32381 / r32382;
        double r32384 = r32380 / r32382;
        double r32385 = r32380 + r32384;
        double r32386 = r32383 / r32385;
        double r32387 = r32381 - r32386;
        double r32388 = r32387 * r32387;
        double r32389 = r32380 + r32388;
        double r32390 = r32381 + r32388;
        double r32391 = r32389 / r32390;
        return r32391;
}
↓
double f(double t) {
        double r32392 = 1.0;
        double r32393 = 2.0;
        double r32394 = t;
        double r32395 = r32392 / r32394;
        double r32396 = r32395 + r32392;
        double r32397 = r32393 / r32396;
        double r32398 = r32397 / r32394;
        double r32399 = r32393 - r32398;
        double r32400 = r32399 * r32399;
        double r32401 = r32392 + r32400;
        double r32402 = r32393 + r32400;
        double r32403 = r32401 / r32402;
        return r32403;
}

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

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (t)
  :name "Kahan p13 Example 2"
  (/ (+ 1.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))) (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))))))