Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
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 r34936 = 1.0;
        double r34937 = 2.0;
        double r34938 = t;
        double r34939 = r34937 / r34938;
        double r34940 = r34936 / r34938;
        double r34941 = r34936 + r34940;
        double r34942 = r34939 / r34941;
        double r34943 = r34937 - r34942;
        double r34944 = r34943 * r34943;
        double r34945 = r34937 + r34944;
        double r34946 = r34936 / r34945;
        double r34947 = r34936 - r34946;
        return r34947;
}
↓
double f(double t) {
        double r34948 = 1.0;
        double r34949 = 2.0;
        double r34950 = t;
        double r34951 = r34949 / r34950;
        double r34952 = r34948 / r34950;
        double r34953 = r34948 + r34952;
        double r34954 = r34951 / r34953;
        double r34955 = r34949 - r34954;
        double r34956 = r34955 * r34955;
        double r34957 = r34949 + r34956;
        double r34958 = r34948 / r34957;
        double r34959 = r34948 - r34958;
        return r34959;
}

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 2020021 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))