Average Error: 0.0 → 0.0
Time: 10.0s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]
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}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}
double f(double t) {
        double r1477494 = 1.0;
        double r1477495 = 2.0;
        double r1477496 = t;
        double r1477497 = r1477495 / r1477496;
        double r1477498 = r1477494 / r1477496;
        double r1477499 = r1477494 + r1477498;
        double r1477500 = r1477497 / r1477499;
        double r1477501 = r1477495 - r1477500;
        double r1477502 = r1477501 * r1477501;
        double r1477503 = r1477495 + r1477502;
        double r1477504 = r1477494 / r1477503;
        double r1477505 = r1477494 - r1477504;
        return r1477505;
}
↓
double f(double t) {
        double r1477506 = 1.0;
        double r1477507 = 2.0;
        double r1477508 = t;
        double r1477509 = r1477506 + r1477508;
        double r1477510 = r1477507 / r1477509;
        double r1477511 = r1477507 - r1477510;
        double r1477512 = r1477511 * r1477511;
        double r1477513 = r1477507 + r1477512;
        double r1477514 = r1477506 / r1477513;
        double r1477515 = r1477506 - r1477514;
        return r1477515;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019129 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))