Average Error: 0.0 → 0.0
Time: 29.9s
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 r3149789 = 1.0;
        double r3149790 = 2.0;
        double r3149791 = t;
        double r3149792 = r3149790 / r3149791;
        double r3149793 = r3149789 / r3149791;
        double r3149794 = r3149789 + r3149793;
        double r3149795 = r3149792 / r3149794;
        double r3149796 = r3149790 - r3149795;
        double r3149797 = r3149796 * r3149796;
        double r3149798 = r3149790 + r3149797;
        double r3149799 = r3149789 / r3149798;
        double r3149800 = r3149789 - r3149799;
        return r3149800;
}
↓
double f(double t) {
        double r3149801 = 1.0;
        double r3149802 = 2.0;
        double r3149803 = t;
        double r3149804 = r3149801 + r3149803;
        double r3149805 = r3149802 / r3149804;
        double r3149806 = r3149802 - r3149805;
        double r3149807 = r3149806 * r3149806;
        double r3149808 = r3149802 + r3149807;
        double r3149809 = r3149801 / r3149808;
        double r3149810 = r3149801 - r3149809;
        return r3149810;
}

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

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

  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 2019125 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))