Average Error: 0.0 → 0.0
Time: 21.1s
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 r4341322 = 1.0;
        double r4341323 = 2.0;
        double r4341324 = t;
        double r4341325 = r4341323 / r4341324;
        double r4341326 = r4341322 / r4341324;
        double r4341327 = r4341322 + r4341326;
        double r4341328 = r4341325 / r4341327;
        double r4341329 = r4341323 - r4341328;
        double r4341330 = r4341329 * r4341329;
        double r4341331 = r4341323 + r4341330;
        double r4341332 = r4341322 / r4341331;
        double r4341333 = r4341322 - r4341332;
        return r4341333;
}
↓
double f(double t) {
        double r4341334 = 1.0;
        double r4341335 = 2.0;
        double r4341336 = t;
        double r4341337 = r4341335 / r4341336;
        double r4341338 = r4341334 / r4341336;
        double r4341339 = r4341334 + r4341338;
        double r4341340 = r4341337 / r4341339;
        double r4341341 = r4341335 - r4341340;
        double r4341342 = r4341341 * r4341341;
        double r4341343 = r4341335 + r4341342;
        double r4341344 = r4341334 / r4341343;
        double r4341345 = r4341334 - r4341344;
        return r4341345;
}

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 2019107 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))