Average Error: 0.0 → 0.0
Time: 1.4s
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 r36153 = 1.0;
        double r36154 = 2.0;
        double r36155 = t;
        double r36156 = r36154 / r36155;
        double r36157 = r36153 / r36155;
        double r36158 = r36153 + r36157;
        double r36159 = r36156 / r36158;
        double r36160 = r36154 - r36159;
        double r36161 = r36160 * r36160;
        double r36162 = r36154 + r36161;
        double r36163 = r36153 / r36162;
        double r36164 = r36153 - r36163;
        return r36164;
}
↓
double f(double t) {
        double r36165 = 1.0;
        double r36166 = 2.0;
        double r36167 = t;
        double r36168 = r36166 / r36167;
        double r36169 = r36165 / r36167;
        double r36170 = r36165 + r36169;
        double r36171 = r36168 / r36170;
        double r36172 = r36166 - r36171;
        double r36173 = r36172 * r36172;
        double r36174 = r36166 + r36173;
        double r36175 = r36165 / r36174;
        double r36176 = r36165 - r36175;
        return r36176;
}

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 2020056 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))