Average Error: 0.0 → 0.0
Time: 9.2s
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 r90121 = 1.0;
        double r90122 = 2.0;
        double r90123 = t;
        double r90124 = r90122 / r90123;
        double r90125 = r90121 / r90123;
        double r90126 = r90121 + r90125;
        double r90127 = r90124 / r90126;
        double r90128 = r90122 - r90127;
        double r90129 = r90128 * r90128;
        double r90130 = r90122 + r90129;
        double r90131 = r90121 / r90130;
        double r90132 = r90121 - r90131;
        return r90132;
}
↓
double f(double t) {
        double r90133 = 1.0;
        double r90134 = 2.0;
        double r90135 = t;
        double r90136 = r90134 / r90135;
        double r90137 = r90133 / r90135;
        double r90138 = r90133 + r90137;
        double r90139 = r90136 / r90138;
        double r90140 = r90134 - r90139;
        double r90141 = r90140 * r90140;
        double r90142 = r90134 + r90141;
        double r90143 = r90133 / r90142;
        double r90144 = r90133 - r90143;
        return r90144;
}

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 2020043 +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)))))))))