Average Error: 0.0 → 0.0
Time: 4.2s
Precision: 64
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[\frac{1 + \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) \cdot \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right)}{2 + \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) \cdot \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right)}\]
\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)}{2 + \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) \cdot \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right)}
double f(double t) {
        double r32509 = 1.0;
        double r32510 = 2.0;
        double r32511 = t;
        double r32512 = r32510 / r32511;
        double r32513 = r32509 / r32511;
        double r32514 = r32509 + r32513;
        double r32515 = r32512 / r32514;
        double r32516 = r32510 - r32515;
        double r32517 = r32516 * r32516;
        double r32518 = r32509 + r32517;
        double r32519 = r32510 + r32517;
        double r32520 = r32518 / r32519;
        return r32520;
}
↓
double f(double t) {
        double r32521 = 1.0;
        double r32522 = 2.0;
        double r32523 = t;
        double r32524 = 1.0;
        double r32525 = r32523 + r32524;
        double r32526 = r32521 * r32525;
        double r32527 = r32522 / r32526;
        double r32528 = r32522 - r32527;
        double r32529 = r32528 * r32528;
        double r32530 = r32521 + r32529;
        double r32531 = r32522 + r32529;
        double r32532 = r32530 / r32531;
        return r32532;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(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))))))))