Average Error: 0.0 → 0.0
Time: 10.2s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]
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{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}
double f(double t) {
        double r1487826 = 1.0;
        double r1487827 = 2.0;
        double r1487828 = t;
        double r1487829 = r1487827 / r1487828;
        double r1487830 = r1487826 / r1487828;
        double r1487831 = r1487826 + r1487830;
        double r1487832 = r1487829 / r1487831;
        double r1487833 = r1487827 - r1487832;
        double r1487834 = r1487833 * r1487833;
        double r1487835 = r1487827 + r1487834;
        double r1487836 = r1487826 / r1487835;
        double r1487837 = r1487826 - r1487836;
        return r1487837;
}
↓
double f(double t) {
        double r1487838 = 1.0;
        double r1487839 = 2.0;
        double r1487840 = t;
        double r1487841 = r1487838 + r1487840;
        double r1487842 = r1487839 / r1487841;
        double r1487843 = r1487839 - r1487842;
        double r1487844 = r1487843 * r1487843;
        double r1487845 = r1487839 + r1487844;
        double r1487846 = r1487838 / r1487845;
        double r1487847 = r1487838 - r1487846;
        return r1487847;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))