Average Error: 0.0 → 0.0
Time: 8.9s
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 r1191233 = 1.0;
        double r1191234 = 2.0;
        double r1191235 = t;
        double r1191236 = r1191234 / r1191235;
        double r1191237 = r1191233 / r1191235;
        double r1191238 = r1191233 + r1191237;
        double r1191239 = r1191236 / r1191238;
        double r1191240 = r1191234 - r1191239;
        double r1191241 = r1191240 * r1191240;
        double r1191242 = r1191234 + r1191241;
        double r1191243 = r1191233 / r1191242;
        double r1191244 = r1191233 - r1191243;
        return r1191244;
}
↓
double f(double t) {
        double r1191245 = 1.0;
        double r1191246 = 2.0;
        double r1191247 = t;
        double r1191248 = r1191245 + r1191247;
        double r1191249 = r1191246 / r1191248;
        double r1191250 = r1191246 - r1191249;
        double r1191251 = r1191250 * r1191250;
        double r1191252 = r1191246 + r1191251;
        double r1191253 = r1191245 / r1191252;
        double r1191254 = r1191245 - r1191253;
        return r1191254;
}

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 2019138 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))