Average Error: 0.0 → 0.0
Time: 11.4s
Precision: 64
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[\frac{1 + \left(2 - \frac{2}{1 + t \cdot 1}\right) \cdot \left(2 - \frac{2}{1 + t \cdot 1}\right)}{2 + \left(2 - \frac{2}{1 + t \cdot 1}\right) \cdot \left(2 - \frac{2}{1 + t \cdot 1}\right)}\]
\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
↓
\frac{1 + \left(2 - \frac{2}{1 + t \cdot 1}\right) \cdot \left(2 - \frac{2}{1 + t \cdot 1}\right)}{2 + \left(2 - \frac{2}{1 + t \cdot 1}\right) \cdot \left(2 - \frac{2}{1 + t \cdot 1}\right)}
double f(double t) {
        double r35098 = 1.0;
        double r35099 = 2.0;
        double r35100 = t;
        double r35101 = r35099 / r35100;
        double r35102 = r35098 / r35100;
        double r35103 = r35098 + r35102;
        double r35104 = r35101 / r35103;
        double r35105 = r35099 - r35104;
        double r35106 = r35105 * r35105;
        double r35107 = r35098 + r35106;
        double r35108 = r35099 + r35106;
        double r35109 = r35107 / r35108;
        return r35109;
}
↓
double f(double t) {
        double r35110 = 1.0;
        double r35111 = 2.0;
        double r35112 = t;
        double r35113 = r35112 * r35110;
        double r35114 = r35110 + r35113;
        double r35115 = r35111 / r35114;
        double r35116 = r35111 - r35115;
        double r35117 = r35116 * r35116;
        double r35118 = r35110 + r35117;
        double r35119 = r35111 + r35117;
        double r35120 = r35118 / r35119;
        return r35120;
}

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

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(FPCore (t)
  :name "Kahan p13 Example 2"
  :precision binary64
  (/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))))))