Average Error: 0.0 → 0.0
Time: 6.8s
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 r22761 = 1.0;
        double r22762 = 2.0;
        double r22763 = t;
        double r22764 = r22762 / r22763;
        double r22765 = r22761 / r22763;
        double r22766 = r22761 + r22765;
        double r22767 = r22764 / r22766;
        double r22768 = r22762 - r22767;
        double r22769 = r22768 * r22768;
        double r22770 = r22762 + r22769;
        double r22771 = r22761 / r22770;
        double r22772 = r22761 - r22771;
        return r22772;
}
↓
double f(double t) {
        double r22773 = 1.0;
        double r22774 = 2.0;
        double r22775 = t;
        double r22776 = r22774 / r22775;
        double r22777 = r22773 / r22775;
        double r22778 = r22773 + r22777;
        double r22779 = r22776 / r22778;
        double r22780 = r22774 - r22779;
        double r22781 = r22780 * r22780;
        double r22782 = r22774 + r22781;
        double r22783 = r22773 / r22782;
        double r22784 = r22773 - r22783;
        return r22784;
}

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 2019194 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1.0 (/ 1.0 (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))))))