Average Error: 0.0 → 0.0
Time: 4.3s
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 r30985 = 1.0;
        double r30986 = 2.0;
        double r30987 = t;
        double r30988 = r30986 / r30987;
        double r30989 = r30985 / r30987;
        double r30990 = r30985 + r30989;
        double r30991 = r30988 / r30990;
        double r30992 = r30986 - r30991;
        double r30993 = r30992 * r30992;
        double r30994 = r30986 + r30993;
        double r30995 = r30985 / r30994;
        double r30996 = r30985 - r30995;
        return r30996;
}
↓
double f(double t) {
        double r30997 = 1.0;
        double r30998 = 2.0;
        double r30999 = t;
        double r31000 = r30998 / r30999;
        double r31001 = r30997 / r30999;
        double r31002 = r30997 + r31001;
        double r31003 = r31000 / r31002;
        double r31004 = r30998 - r31003;
        double r31005 = r31004 * r31004;
        double r31006 = r30998 + r31005;
        double r31007 = r30997 / r31006;
        double r31008 = r30997 - r31007;
        return r31008;
}

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 2019304 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))