Average Error: 0.0 → 0.0
Time: 1.6s
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 r32109 = 1.0;
        double r32110 = 2.0;
        double r32111 = t;
        double r32112 = r32110 / r32111;
        double r32113 = r32109 / r32111;
        double r32114 = r32109 + r32113;
        double r32115 = r32112 / r32114;
        double r32116 = r32110 - r32115;
        double r32117 = r32116 * r32116;
        double r32118 = r32110 + r32117;
        double r32119 = r32109 / r32118;
        double r32120 = r32109 - r32119;
        return r32120;
}
↓
double f(double t) {
        double r32121 = 1.0;
        double r32122 = 2.0;
        double r32123 = t;
        double r32124 = r32122 / r32123;
        double r32125 = r32121 / r32123;
        double r32126 = r32121 + r32125;
        double r32127 = r32124 / r32126;
        double r32128 = r32122 - r32127;
        double r32129 = r32128 * r32128;
        double r32130 = r32122 + r32129;
        double r32131 = r32121 / r32130;
        double r32132 = r32121 - r32131;
        return r32132;
}

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 2020036 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))