\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\begin{array}{l}
\mathbf{if}\;\alpha \le 8.836463279649086 \cdot 10^{+162}:\\
\;\;\;\;\frac{\frac{\frac{1.0 + \left(\beta \cdot \alpha + \left(\beta + \alpha\right)\right)}{\left(\beta + \alpha\right) + 2}}{\left(\beta + \alpha\right) + 2}}{1.0 + \left(\left(\beta + \alpha\right) + 2\right)}\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{\left(1 - \frac{1.0}{\alpha}\right) + \frac{2.0}{\alpha \cdot \alpha}}{\left(\beta + \alpha\right) + 2}}{1.0 + \left(\left(\beta + \alpha\right) + 2\right)}\\
\end{array}double f(double alpha, double beta) {
double r2302962 = alpha;
double r2302963 = beta;
double r2302964 = r2302962 + r2302963;
double r2302965 = r2302963 * r2302962;
double r2302966 = r2302964 + r2302965;
double r2302967 = 1.0;
double r2302968 = r2302966 + r2302967;
double r2302969 = 2.0;
double r2302970 = 1.0;
double r2302971 = r2302969 * r2302970;
double r2302972 = r2302964 + r2302971;
double r2302973 = r2302968 / r2302972;
double r2302974 = r2302973 / r2302972;
double r2302975 = r2302972 + r2302967;
double r2302976 = r2302974 / r2302975;
return r2302976;
}
double f(double alpha, double beta) {
double r2302977 = alpha;
double r2302978 = 8.836463279649086e+162;
bool r2302979 = r2302977 <= r2302978;
double r2302980 = 1.0;
double r2302981 = beta;
double r2302982 = r2302981 * r2302977;
double r2302983 = r2302981 + r2302977;
double r2302984 = r2302982 + r2302983;
double r2302985 = r2302980 + r2302984;
double r2302986 = 2.0;
double r2302987 = r2302983 + r2302986;
double r2302988 = r2302985 / r2302987;
double r2302989 = r2302988 / r2302987;
double r2302990 = r2302980 + r2302987;
double r2302991 = r2302989 / r2302990;
double r2302992 = 1.0;
double r2302993 = r2302980 / r2302977;
double r2302994 = r2302992 - r2302993;
double r2302995 = 2.0;
double r2302996 = r2302977 * r2302977;
double r2302997 = r2302995 / r2302996;
double r2302998 = r2302994 + r2302997;
double r2302999 = r2302998 / r2302987;
double r2303000 = r2302999 / r2302990;
double r2303001 = r2302979 ? r2302991 : r2303000;
return r2303001;
}



Bits error versus alpha



Bits error versus beta
Results
if alpha < 8.836463279649086e+162Initial program 1.3
rmApplied +-commutative1.3
if 8.836463279649086e+162 < alpha Initial program 16.3
Taylor expanded around inf 8.0
Simplified8.0
Final simplification2.3
herbie shell --seed 2019154
(FPCore (alpha beta)
:name "Octave 3.8, jcobi/3"
:pre (and (> alpha -1) (> beta -1))
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))