Average Error: 0.0 → 0.0
Time: 15.5s
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 r47395 = 1.0;
        double r47396 = 2.0;
        double r47397 = t;
        double r47398 = r47396 / r47397;
        double r47399 = r47395 / r47397;
        double r47400 = r47395 + r47399;
        double r47401 = r47398 / r47400;
        double r47402 = r47396 - r47401;
        double r47403 = r47402 * r47402;
        double r47404 = r47396 + r47403;
        double r47405 = r47395 / r47404;
        double r47406 = r47395 - r47405;
        return r47406;
}
↓
double f(double t) {
        double r47407 = 1.0;
        double r47408 = 2.0;
        double r47409 = t;
        double r47410 = r47408 / r47409;
        double r47411 = r47407 / r47409;
        double r47412 = r47407 + r47411;
        double r47413 = r47410 / r47412;
        double r47414 = r47408 - r47413;
        double r47415 = r47414 * r47414;
        double r47416 = r47408 + r47415;
        double r47417 = r47407 / r47416;
        double r47418 = r47407 - r47417;
        return r47418;
}

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 2019212 +o rules:numerics
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))