Average Error: 0.0 → 0.0
Time: 2.3s
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 r46084 = 1.0;
        double r46085 = 2.0;
        double r46086 = t;
        double r46087 = r46085 / r46086;
        double r46088 = r46084 / r46086;
        double r46089 = r46084 + r46088;
        double r46090 = r46087 / r46089;
        double r46091 = r46085 - r46090;
        double r46092 = r46091 * r46091;
        double r46093 = r46085 + r46092;
        double r46094 = r46084 / r46093;
        double r46095 = r46084 - r46094;
        return r46095;
}
↓
double f(double t) {
        double r46096 = 1.0;
        double r46097 = 2.0;
        double r46098 = t;
        double r46099 = r46097 / r46098;
        double r46100 = r46096 / r46098;
        double r46101 = r46096 + r46100;
        double r46102 = r46099 / r46101;
        double r46103 = r46097 - r46102;
        double r46104 = r46103 * r46103;
        double r46105 = r46097 + r46104;
        double r46106 = r46096 / r46105;
        double r46107 = r46096 - r46106;
        return r46107;
}

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 2020024 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))