Average Error: 0.0 → 0.0
Time: 3.8s
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 r46243 = 1.0;
        double r46244 = 2.0;
        double r46245 = t;
        double r46246 = r46244 / r46245;
        double r46247 = r46243 / r46245;
        double r46248 = r46243 + r46247;
        double r46249 = r46246 / r46248;
        double r46250 = r46244 - r46249;
        double r46251 = r46250 * r46250;
        double r46252 = r46244 + r46251;
        double r46253 = r46243 / r46252;
        double r46254 = r46243 - r46253;
        return r46254;
}
↓
double f(double t) {
        double r46255 = 1.0;
        double r46256 = 2.0;
        double r46257 = t;
        double r46258 = r46256 / r46257;
        double r46259 = r46255 / r46257;
        double r46260 = r46255 + r46259;
        double r46261 = r46258 / r46260;
        double r46262 = r46256 - r46261;
        double r46263 = r46262 * r46262;
        double r46264 = r46256 + r46263;
        double r46265 = r46255 / r46264;
        double r46266 = r46255 - r46265;
        return r46266;
}

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 2020060 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))