Average Error: 0.2 → 0.2
Time: 3.7s
Precision: 64
\[\frac{e^{x}}{e^{x} + e^{y}}\]
\[\frac{e^{x}}{e^{x} + e^{y}}\]
\frac{e^{x}}{e^{x} + e^{y}}
\frac{e^{x}}{e^{x} + e^{y}}
double f(double x, double y) {
        double r1791891 = x;
        double r1791892 = exp(r1791891);
        double r1791893 = y;
        double r1791894 = exp(r1791893);
        double r1791895 = r1791892 + r1791894;
        double r1791896 = r1791892 / r1791895;
        return r1791896;
}

double f(double x, double y) {
        double r1791897 = x;
        double r1791898 = exp(r1791897);
        double r1791899 = y;
        double r1791900 = exp(r1791899);
        double r1791901 = r1791898 + r1791900;
        double r1791902 = r1791898 / r1791901;
        return r1791902;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{e^{x}}{e^{x} + e^{y}}\]
  2. Final simplification0.2

    \[\leadsto \frac{e^{x}}{e^{x} + e^{y}}\]

Reproduce

herbie shell --seed 1 
(FPCore (x y)
  :name "exp(x) / (exp(x) + exp(y))"
  :precision binary32
  (/ (exp x) (+ (exp x) (exp y))))