Average Error: 0.0 → 0.0
Time: 7.1s
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 r27222 = 1.0;
        double r27223 = 2.0;
        double r27224 = t;
        double r27225 = r27223 / r27224;
        double r27226 = r27222 / r27224;
        double r27227 = r27222 + r27226;
        double r27228 = r27225 / r27227;
        double r27229 = r27223 - r27228;
        double r27230 = r27229 * r27229;
        double r27231 = r27223 + r27230;
        double r27232 = r27222 / r27231;
        double r27233 = r27222 - r27232;
        return r27233;
}
↓
double f(double t) {
        double r27234 = 1.0;
        double r27235 = 2.0;
        double r27236 = t;
        double r27237 = r27235 / r27236;
        double r27238 = r27234 / r27236;
        double r27239 = r27234 + r27238;
        double r27240 = r27237 / r27239;
        double r27241 = r27235 - r27240;
        double r27242 = r27241 * r27241;
        double r27243 = r27235 + r27242;
        double r27244 = r27234 / r27243;
        double r27245 = r27234 - r27244;
        return r27245;
}

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 2019208 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))