Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]
\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{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}
double f(double t) {
        double r716983 = 1.0;
        double r716984 = 2.0;
        double r716985 = t;
        double r716986 = r716984 * r716985;
        double r716987 = r716983 + r716985;
        double r716988 = r716986 / r716987;
        double r716989 = r716988 * r716988;
        double r716990 = r716983 + r716989;
        double r716991 = r716984 + r716989;
        double r716992 = r716990 / r716991;
        return r716992;
}
↓
double f(double t) {
        double r716993 = 1.0;
        double r716994 = t;
        double r716995 = 2.0;
        double r716996 = r716994 * r716995;
        double r716997 = r716993 + r716994;
        double r716998 = r716996 / r716997;
        double r716999 = r716998 * r716998;
        double r717000 = r716993 + r716999;
        double r717001 = r716995 + r716999;
        double r717002 = r717000 / r717001;
        return r717002;
}

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

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

Reproduce

herbie shell --seed 2019154 
(FPCore (t)
  :name "Kahan p13 Example 1"
  (/ (+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))) (+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))))