Average Error: 0.0 → 0.0
Time: 6.3s
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 r41058 = 1.0;
        double r41059 = 2.0;
        double r41060 = t;
        double r41061 = r41059 / r41060;
        double r41062 = r41058 / r41060;
        double r41063 = r41058 + r41062;
        double r41064 = r41061 / r41063;
        double r41065 = r41059 - r41064;
        double r41066 = r41065 * r41065;
        double r41067 = r41059 + r41066;
        double r41068 = r41058 / r41067;
        double r41069 = r41058 - r41068;
        return r41069;
}
↓
double f(double t) {
        double r41070 = 1.0;
        double r41071 = 2.0;
        double r41072 = t;
        double r41073 = r41071 / r41072;
        double r41074 = r41070 / r41072;
        double r41075 = r41070 + r41074;
        double r41076 = r41073 / r41075;
        double r41077 = r41071 - r41076;
        double r41078 = r41077 * r41077;
        double r41079 = r41071 + r41078;
        double r41080 = r41070 / r41079;
        double r41081 = r41070 - r41080;
        return r41081;
}

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 2020100 +o rules:numerics
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))