Average Error: 0.0 → 0.0
Time: 21.5s
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 r4341317 = 1.0;
        double r4341318 = 2.0;
        double r4341319 = t;
        double r4341320 = r4341318 / r4341319;
        double r4341321 = r4341317 / r4341319;
        double r4341322 = r4341317 + r4341321;
        double r4341323 = r4341320 / r4341322;
        double r4341324 = r4341318 - r4341323;
        double r4341325 = r4341324 * r4341324;
        double r4341326 = r4341318 + r4341325;
        double r4341327 = r4341317 / r4341326;
        double r4341328 = r4341317 - r4341327;
        return r4341328;
}
↓
double f(double t) {
        double r4341329 = 1.0;
        double r4341330 = 2.0;
        double r4341331 = t;
        double r4341332 = r4341330 / r4341331;
        double r4341333 = r4341329 / r4341331;
        double r4341334 = r4341329 + r4341333;
        double r4341335 = r4341332 / r4341334;
        double r4341336 = r4341330 - r4341335;
        double r4341337 = r4341336 * r4341336;
        double r4341338 = r4341330 + r4341337;
        double r4341339 = r4341329 / r4341338;
        double r4341340 = r4341329 - r4341339;
        return r4341340;
}

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 2019107 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))