Average Error: 0.0 → 0.0
Time: 8.5s
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 r1716782 = 1.0;
        double r1716783 = 2.0;
        double r1716784 = t;
        double r1716785 = r1716783 / r1716784;
        double r1716786 = r1716782 / r1716784;
        double r1716787 = r1716782 + r1716786;
        double r1716788 = r1716785 / r1716787;
        double r1716789 = r1716783 - r1716788;
        double r1716790 = r1716789 * r1716789;
        double r1716791 = r1716783 + r1716790;
        double r1716792 = r1716782 / r1716791;
        double r1716793 = r1716782 - r1716792;
        return r1716793;
}
↓
double f(double t) {
        double r1716794 = 1.0;
        double r1716795 = -2.0;
        double r1716796 = t;
        double r1716797 = r1716794 + r1716796;
        double r1716798 = r1716795 / r1716797;
        double r1716799 = r1716795 - r1716798;
        double r1716800 = r1716799 * r1716799;
        double r1716801 = r1716800 - r1716795;
        double r1716802 = r1716794 / r1716801;
        double r1716803 = r1716794 - r1716802;
        return r1716803;
}

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 2019164 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))