Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}
↓
\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}
double f(double t) {
        double r47325 = 1.0;
        double r47326 = 2.0;
        double r47327 = t;
        double r47328 = r47326 * r47327;
        double r47329 = r47325 + r47327;
        double r47330 = r47328 / r47329;
        double r47331 = r47330 * r47330;
        double r47332 = r47325 + r47331;
        double r47333 = r47326 + r47331;
        double r47334 = r47332 / r47333;
        return r47334;
}
↓
double f(double t) {
        double r47335 = 1.0;
        double r47336 = 2.0;
        double r47337 = t;
        double r47338 = r47336 * r47337;
        double r47339 = r47335 + r47337;
        double r47340 = r47338 / r47339;
        double r47341 = r47340 * r47340;
        double r47342 = r47335 + r47341;
        double r47343 = r47336 + r47341;
        double r47344 = r47342 / r47343;
        return r47344;
}

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

    \[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

  2. Final simplification0.0

    \[\leadsto \frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

Reproduce

herbie shell --seed 2019350 
(FPCore (t)
  :name "Kahan p13 Example 1"
  :precision binary64
  (/ (+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))) (+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))))