Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
1 - \frac{1}{2 + \left(2 - \frac{\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{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
double f(double t) {
        double r25327 = 1.0;
        double r25328 = 2.0;
        double r25329 = t;
        double r25330 = r25328 / r25329;
        double r25331 = r25327 / r25329;
        double r25332 = r25327 + r25331;
        double r25333 = r25330 / r25332;
        double r25334 = r25328 - r25333;
        double r25335 = r25334 * r25334;
        double r25336 = r25328 + r25335;
        double r25337 = r25327 / r25336;
        double r25338 = r25327 - r25337;
        return r25338;
}
↓
double f(double t) {
        double r25339 = 1.0;
        double r25340 = 2.0;
        double r25341 = t;
        double r25342 = r25340 / r25341;
        double r25343 = r25339 / r25341;
        double r25344 = r25339 + r25343;
        double r25345 = r25342 / r25344;
        double r25346 = r25340 - r25345;
        double r25347 = r25346 * r25346;
        double r25348 = r25340 + r25347;
        double r25349 = r25339 / r25348;
        double r25350 = r25339 - r25349;
        return r25350;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))