Average Error: 0.0 → 0.0
Time: 17.8s
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 r1980940 = 1.0;
        double r1980941 = 2.0;
        double r1980942 = t;
        double r1980943 = r1980941 / r1980942;
        double r1980944 = r1980940 / r1980942;
        double r1980945 = r1980940 + r1980944;
        double r1980946 = r1980943 / r1980945;
        double r1980947 = r1980941 - r1980946;
        double r1980948 = r1980947 * r1980947;
        double r1980949 = r1980941 + r1980948;
        double r1980950 = r1980940 / r1980949;
        double r1980951 = r1980940 - r1980950;
        return r1980951;
}
↓
double f(double t) {
        double r1980952 = 1.0;
        double r1980953 = 2.0;
        double r1980954 = t;
        double r1980955 = r1980952 + r1980954;
        double r1980956 = r1980953 / r1980955;
        double r1980957 = r1980953 - r1980956;
        double r1980958 = r1980957 * r1980957;
        double r1980959 = r1980953 + r1980958;
        double r1980960 = r1980952 / r1980959;
        double r1980961 = r1980952 - r1980960;
        return r1980961;
}

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 2019104 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))