Average Error: 0.0 → 0.0
Time: 8.7s
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 r786931 = 1.0;
        double r786932 = 2.0;
        double r786933 = t;
        double r786934 = r786932 / r786933;
        double r786935 = r786931 / r786933;
        double r786936 = r786931 + r786935;
        double r786937 = r786934 / r786936;
        double r786938 = r786932 - r786937;
        double r786939 = r786938 * r786938;
        double r786940 = r786932 + r786939;
        double r786941 = r786931 / r786940;
        double r786942 = r786931 - r786941;
        return r786942;
}
↓
double f(double t) {
        double r786943 = 1.0;
        double r786944 = 2.0;
        double r786945 = t;
        double r786946 = r786943 + r786945;
        double r786947 = r786944 / r786946;
        double r786948 = r786944 - r786947;
        double r786949 = r786948 * r786948;
        double r786950 = r786944 + r786949;
        double r786951 = r786943 / r786950;
        double r786952 = r786943 - r786951;
        return r786952;
}

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 2019149 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))