Average Error: 0.0 → 0.0
Time: 5.2s
Precision: 64
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[\frac{1 + \left(\frac{-2}{1 + t} - -2\right) \cdot \left(\frac{-2}{1 + t} - -2\right)}{\left(\frac{-2}{1 + t} - -2\right) \cdot \left(\frac{-2}{1 + t} - -2\right) - -2}\]
\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
↓
\frac{1 + \left(\frac{-2}{1 + t} - -2\right) \cdot \left(\frac{-2}{1 + t} - -2\right)}{\left(\frac{-2}{1 + t} - -2\right) \cdot \left(\frac{-2}{1 + t} - -2\right) - -2}
double f(double t) {
        double r1283559 = 1.0;
        double r1283560 = 2.0;
        double r1283561 = t;
        double r1283562 = r1283560 / r1283561;
        double r1283563 = r1283559 / r1283561;
        double r1283564 = r1283559 + r1283563;
        double r1283565 = r1283562 / r1283564;
        double r1283566 = r1283560 - r1283565;
        double r1283567 = r1283566 * r1283566;
        double r1283568 = r1283559 + r1283567;
        double r1283569 = r1283560 + r1283567;
        double r1283570 = r1283568 / r1283569;
        return r1283570;
}
↓
double f(double t) {
        double r1283571 = 1.0;
        double r1283572 = -2.0;
        double r1283573 = t;
        double r1283574 = r1283571 + r1283573;
        double r1283575 = r1283572 / r1283574;
        double r1283576 = r1283575 - r1283572;
        double r1283577 = r1283576 * r1283576;
        double r1283578 = r1283571 + r1283577;
        double r1283579 = r1283577 - r1283572;
        double r1283580 = r1283578 / r1283579;
        return r1283580;
}

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

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019129 
(FPCore (t)
  :name "Kahan p13 Example 2"
  (/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))))))