Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[\frac{1 + \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) \cdot \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right)}{\left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) \cdot \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) + 2}\]
\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(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) \cdot \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right)}{\left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) \cdot \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) + 2}
double f(double t) {
        double r23511 = 1.0;
        double r23512 = 2.0;
        double r23513 = t;
        double r23514 = r23512 / r23513;
        double r23515 = r23511 / r23513;
        double r23516 = r23511 + r23515;
        double r23517 = r23514 / r23516;
        double r23518 = r23512 - r23517;
        double r23519 = r23518 * r23518;
        double r23520 = r23511 + r23519;
        double r23521 = r23512 + r23519;
        double r23522 = r23520 / r23521;
        return r23522;
}
↓
double f(double t) {
        double r23523 = 1.0;
        double r23524 = 2.0;
        double r23525 = t;
        double r23526 = 1.0;
        double r23527 = r23525 + r23526;
        double r23528 = r23523 * r23527;
        double r23529 = r23524 / r23528;
        double r23530 = r23524 - r23529;
        double r23531 = r23530 * r23530;
        double r23532 = r23523 + r23531;
        double r23533 = r23531 + r23524;
        double r23534 = r23532 / r23533;
        return r23534;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (t)
  :name "Kahan p13 Example 2"
  :precision binary64
  (/ (+ 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))))))))