Average Error: 0.0 → 0.0
Time: 23.5s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]
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{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}
double f(double t) {
        double r3629160 = 1.0;
        double r3629161 = 2.0;
        double r3629162 = t;
        double r3629163 = r3629161 / r3629162;
        double r3629164 = r3629160 / r3629162;
        double r3629165 = r3629160 + r3629164;
        double r3629166 = r3629163 / r3629165;
        double r3629167 = r3629161 - r3629166;
        double r3629168 = r3629167 * r3629167;
        double r3629169 = r3629161 + r3629168;
        double r3629170 = r3629160 / r3629169;
        double r3629171 = r3629160 - r3629170;
        return r3629171;
}
↓
double f(double t) {
        double r3629172 = 1.0;
        double r3629173 = 2.0;
        double r3629174 = t;
        double r3629175 = r3629172 + r3629174;
        double r3629176 = r3629173 / r3629175;
        double r3629177 = r3629173 - r3629176;
        double r3629178 = r3629177 * r3629177;
        double r3629179 = r3629173 + r3629178;
        double r3629180 = r3629172 / r3629179;
        double r3629181 = r3629172 - r3629180;
        return r3629181;
}

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. Simplified0.0

    \[\leadsto \color{blue}{1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}}\]

  3. Final simplification0.0

    \[\leadsto 1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]

Reproduce

herbie shell --seed 2019124 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))