Average Error: 0.0 → 0.0
Time: 9.9s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{2}{t \cdot 1 + 1}\right) \cdot \left(2 - \frac{2}{t \cdot 1 + 1}\right)}\]
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}{t \cdot 1 + 1}\right) \cdot \left(2 - \frac{2}{t \cdot 1 + 1}\right)}
double f(double t) {
        double r33319 = 1.0;
        double r33320 = 2.0;
        double r33321 = t;
        double r33322 = r33320 / r33321;
        double r33323 = r33319 / r33321;
        double r33324 = r33319 + r33323;
        double r33325 = r33322 / r33324;
        double r33326 = r33320 - r33325;
        double r33327 = r33326 * r33326;
        double r33328 = r33320 + r33327;
        double r33329 = r33319 / r33328;
        double r33330 = r33319 - r33329;
        return r33330;
}
↓
double f(double t) {
        double r33331 = 1.0;
        double r33332 = 2.0;
        double r33333 = t;
        double r33334 = r33333 * r33331;
        double r33335 = r33334 + r33331;
        double r33336 = r33332 / r33335;
        double r33337 = r33332 - r33336;
        double r33338 = r33337 * r33337;
        double r33339 = r33332 + r33338;
        double r33340 = r33331 / r33339;
        double r33341 = r33331 - r33340;
        return r33341;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))