Average Error: 0.0 → 0.0
Time: 4.1s
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 r29523 = 1.0;
        double r29524 = 2.0;
        double r29525 = t;
        double r29526 = r29524 / r29525;
        double r29527 = r29523 / r29525;
        double r29528 = r29523 + r29527;
        double r29529 = r29526 / r29528;
        double r29530 = r29524 - r29529;
        double r29531 = r29530 * r29530;
        double r29532 = r29523 + r29531;
        double r29533 = r29524 + r29531;
        double r29534 = r29532 / r29533;
        return r29534;
}
↓
double f(double t) {
        double r29535 = 1.0;
        double r29536 = 2.0;
        double r29537 = t;
        double r29538 = 1.0;
        double r29539 = r29537 + r29538;
        double r29540 = r29535 * r29539;
        double r29541 = r29536 / r29540;
        double r29542 = r29536 - r29541;
        double r29543 = r29542 * r29542;
        double r29544 = r29535 + r29543;
        double r29545 = r29543 + r29536;
        double r29546 = r29544 / r29545;
        return r29546;
}

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))))))))