Average Error: 0.1 → 0.1
Time: 6.8s
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 r613923 = 1.0;
        double r613924 = 2.0;
        double r613925 = t;
        double r613926 = r613924 * r613925;
        double r613927 = r613923 + r613925;
        double r613928 = r613926 / r613927;
        double r613929 = r613928 * r613928;
        double r613930 = r613923 + r613929;
        double r613931 = r613924 + r613929;
        double r613932 = r613930 / r613931;
        return r613932;
}
↓
double f(double t) {
        double r613933 = 1.0;
        double r613934 = t;
        double r613935 = 2.0;
        double r613936 = r613934 * r613935;
        double r613937 = r613933 + r613934;
        double r613938 = r613936 / r613937;
        double r613939 = r613938 * r613938;
        double r613940 = r613933 + r613939;
        double r613941 = r613935 + r613939;
        double r613942 = r613940 / r613941;
        return r613942;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2019152 
(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))))))