Average Error: 0.0 → 0.0
Time: 10.1s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\left(2 - \frac{2}{t \cdot 1 + 1}\right) \cdot \left(2 - \frac{2}{t \cdot 1 + 1}\right) + 2}\]
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}{\left(2 - \frac{2}{t \cdot 1 + 1}\right) \cdot \left(2 - \frac{2}{t \cdot 1 + 1}\right) + 2}
double f(double t) {
        double r21301 = 1.0;
        double r21302 = 2.0;
        double r21303 = t;
        double r21304 = r21302 / r21303;
        double r21305 = r21301 / r21303;
        double r21306 = r21301 + r21305;
        double r21307 = r21304 / r21306;
        double r21308 = r21302 - r21307;
        double r21309 = r21308 * r21308;
        double r21310 = r21302 + r21309;
        double r21311 = r21301 / r21310;
        double r21312 = r21301 - r21311;
        return r21312;
}
↓
double f(double t) {
        double r21313 = 1.0;
        double r21314 = 2.0;
        double r21315 = t;
        double r21316 = r21315 * r21313;
        double r21317 = r21316 + r21313;
        double r21318 = r21314 / r21317;
        double r21319 = r21314 - r21318;
        double r21320 = r21319 * r21319;
        double r21321 = r21320 + r21314;
        double r21322 = r21313 / r21321;
        double r21323 = r21313 - r21322;
        return r21323;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))