Average Error: 0.0 → 0.0
Time: 10.9s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\frac{\left(2 \cdot 2 - \frac{2}{t + 1} \cdot \frac{2}{t + 1}\right) \cdot \left(2 \cdot 2 - \frac{2}{t + 1} \cdot \frac{2}{t + 1}\right)}{\left(2 + \frac{2}{t + 1}\right) \cdot \left(2 + \frac{2}{t + 1}\right)} + 2}\]
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}{\frac{\left(2 \cdot 2 - \frac{2}{t + 1} \cdot \frac{2}{t + 1}\right) \cdot \left(2 \cdot 2 - \frac{2}{t + 1} \cdot \frac{2}{t + 1}\right)}{\left(2 + \frac{2}{t + 1}\right) \cdot \left(2 + \frac{2}{t + 1}\right)} + 2}
double f(double t) {
        double r945680 = 1.0;
        double r945681 = 2.0;
        double r945682 = t;
        double r945683 = r945681 / r945682;
        double r945684 = r945680 / r945682;
        double r945685 = r945680 + r945684;
        double r945686 = r945683 / r945685;
        double r945687 = r945681 - r945686;
        double r945688 = r945687 * r945687;
        double r945689 = r945681 + r945688;
        double r945690 = r945680 / r945689;
        double r945691 = r945680 - r945690;
        return r945691;
}
↓
double f(double t) {
        double r945692 = 1.0;
        double r945693 = 2.0;
        double r945694 = r945693 * r945693;
        double r945695 = t;
        double r945696 = r945695 + r945692;
        double r945697 = r945693 / r945696;
        double r945698 = r945697 * r945697;
        double r945699 = r945694 - r945698;
        double r945700 = r945699 * r945699;
        double r945701 = r945693 + r945697;
        double r945702 = r945701 * r945701;
        double r945703 = r945700 / r945702;
        double r945704 = r945703 + r945693;
        double r945705 = r945692 / r945704;
        double r945706 = r945692 - r945705;
        return r945706;
}

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. Using strategy rm

  4. Applied flip--0.0

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

  5. Applied flip--0.0

    \[\leadsto 1 - \frac{1}{2 + \color{blue}{\frac{2 \cdot 2 - \frac{2}{1 + t} \cdot \frac{2}{1 + t}}{2 + \frac{2}{1 + t}}} \cdot \frac{2 \cdot 2 - \frac{2}{1 + t} \cdot \frac{2}{1 + t}}{2 + \frac{2}{1 + t}}}\]

  6. Applied frac-times0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))