Average Error: 0.0 → 0.0
Time: 8.2s
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 r24345 = 1.0;
        double r24346 = 2.0;
        double r24347 = t;
        double r24348 = r24346 / r24347;
        double r24349 = r24345 / r24347;
        double r24350 = r24345 + r24349;
        double r24351 = r24348 / r24350;
        double r24352 = r24346 - r24351;
        double r24353 = r24352 * r24352;
        double r24354 = r24346 + r24353;
        double r24355 = r24345 / r24354;
        double r24356 = r24345 - r24355;
        return r24356;
}
↓
double f(double t) {
        double r24357 = 1.0;
        double r24358 = 2.0;
        double r24359 = t;
        double r24360 = r24358 / r24359;
        double r24361 = r24357 / r24359;
        double r24362 = r24357 + r24361;
        double r24363 = r24360 / r24362;
        double r24364 = r24358 - r24363;
        double r24365 = r24364 * r24364;
        double r24366 = r24358 + r24365;
        double r24367 = r24357 / r24366;
        double r24368 = r24357 - r24367;
        return r24368;
}

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 2019291 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))