Average Error: 0.0 → 0.0
Time: 2.2s
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 r33933 = 1.0;
        double r33934 = 2.0;
        double r33935 = t;
        double r33936 = r33934 / r33935;
        double r33937 = r33933 / r33935;
        double r33938 = r33933 + r33937;
        double r33939 = r33936 / r33938;
        double r33940 = r33934 - r33939;
        double r33941 = r33940 * r33940;
        double r33942 = r33934 + r33941;
        double r33943 = r33933 / r33942;
        double r33944 = r33933 - r33943;
        return r33944;
}
↓
double f(double t) {
        double r33945 = 1.0;
        double r33946 = 2.0;
        double r33947 = t;
        double r33948 = r33946 / r33947;
        double r33949 = r33945 / r33947;
        double r33950 = r33945 + r33949;
        double r33951 = r33948 / r33950;
        double r33952 = r33946 - r33951;
        double r33953 = r33952 * r33952;
        double r33954 = r33946 + r33953;
        double r33955 = r33945 / r33954;
        double r33956 = r33945 - r33955;
        return r33956;
}

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 2019322 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))