Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right) - -2}\]
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}{\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right) - -2}
double f(double t) {
        double r1777962 = 1.0;
        double r1777963 = 2.0;
        double r1777964 = t;
        double r1777965 = r1777963 / r1777964;
        double r1777966 = r1777962 / r1777964;
        double r1777967 = r1777962 + r1777966;
        double r1777968 = r1777965 / r1777967;
        double r1777969 = r1777963 - r1777968;
        double r1777970 = r1777969 * r1777969;
        double r1777971 = r1777963 + r1777970;
        double r1777972 = r1777962 / r1777971;
        double r1777973 = r1777962 - r1777972;
        return r1777973;
}
↓
double f(double t) {
        double r1777974 = 1.0;
        double r1777975 = -2.0;
        double r1777976 = t;
        double r1777977 = r1777974 + r1777976;
        double r1777978 = r1777975 / r1777977;
        double r1777979 = r1777975 - r1777978;
        double r1777980 = r1777979 * r1777979;
        double r1777981 = r1777980 - r1777975;
        double r1777982 = r1777974 / r1777981;
        double r1777983 = r1777974 - r1777982;
        return r1777983;
}

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

    \[\leadsto \color{blue}{1 - \frac{1}{\left(-2 - \frac{-2}{t + 1}\right) \cdot \left(-2 - \frac{-2}{t + 1}\right) - -2}}\]

  3. Final simplification0.0

    \[\leadsto 1 - \frac{1}{\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right) - -2}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))