\[ \begin{array}{c}[a, b] = \mathsf{sort}([a, b])\\ \end{array} \]
\[\log \left(e^{a} + e^{b}\right)
\]
↓
\[\mathsf{log1p}\left(e^{a}\right) + \frac{b}{e^{a} + 1}
\]
(FPCore (a b) :precision binary64 (log (+ (exp a) (exp b))))
↓
(FPCore (a b) :precision binary64 (+ (log1p (exp a)) (/ b (+ (exp a) 1.0))))
double code(double a, double b) {
return log((exp(a) + exp(b)));
}
↓
double code(double a, double b) {
return log1p(exp(a)) + (b / (exp(a) + 1.0));
}
public static double code(double a, double b) {
return Math.log((Math.exp(a) + Math.exp(b)));
}
↓
public static double code(double a, double b) {
return Math.log1p(Math.exp(a)) + (b / (Math.exp(a) + 1.0));
}
def code(a, b):
return math.log((math.exp(a) + math.exp(b)))
↓
def code(a, b):
return math.log1p(math.exp(a)) + (b / (math.exp(a) + 1.0))
function code(a, b)
return log(Float64(exp(a) + exp(b)))
end
↓
function code(a, b)
return Float64(log1p(exp(a)) + Float64(b / Float64(exp(a) + 1.0)))
end
code[a_, b_] := N[Log[N[(N[Exp[a], $MachinePrecision] + N[Exp[b], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
↓
code[a_, b_] := N[(N[Log[1 + N[Exp[a], $MachinePrecision]], $MachinePrecision] + N[(b / N[(N[Exp[a], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\log \left(e^{a} + e^{b}\right)
↓
\mathsf{log1p}\left(e^{a}\right) + \frac{b}{e^{a} + 1}
