Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) \cdot \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right)}\]
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 \cdot \left(t + 1\right)}\right) \cdot \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right)}
double f(double t) {
        double r21324 = 1.0;
        double r21325 = 2.0;
        double r21326 = t;
        double r21327 = r21325 / r21326;
        double r21328 = r21324 / r21326;
        double r21329 = r21324 + r21328;
        double r21330 = r21327 / r21329;
        double r21331 = r21325 - r21330;
        double r21332 = r21331 * r21331;
        double r21333 = r21325 + r21332;
        double r21334 = r21324 / r21333;
        double r21335 = r21324 - r21334;
        return r21335;
}
↓
double f(double t) {
        double r21336 = 1.0;
        double r21337 = 2.0;
        double r21338 = t;
        double r21339 = 1.0;
        double r21340 = r21338 + r21339;
        double r21341 = r21336 * r21340;
        double r21342 = r21337 / r21341;
        double r21343 = r21337 - r21342;
        double r21344 = r21343 * r21343;
        double r21345 = r21337 + r21344;
        double r21346 = r21336 / r21345;
        double r21347 = r21336 - r21346;
        return r21347;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))