Average Error: 0.7 → 0.7
Time: 14.6s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}
double f(double a, double b) {
        double r7602588 = a;
        double r7602589 = exp(r7602588);
        double r7602590 = b;
        double r7602591 = exp(r7602590);
        double r7602592 = r7602589 + r7602591;
        double r7602593 = r7602589 / r7602592;
        return r7602593;
}
↓
double f(double a, double b) {
        double r7602594 = a;
        double r7602595 = exp(r7602594);
        double r7602596 = b;
        double r7602597 = exp(r7602596);
        double r7602598 = r7602595 + r7602597;
        double r7602599 = r7602595 / r7602598;
        return r7602599;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.7
Target0.0
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

    \[\frac{e^{a}}{e^{a} + e^{b}}\]

  2. Final simplification0.7

    \[\leadsto \frac{e^{a}}{e^{a} + e^{b}}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1 (+ 1 (exp (- b a))))

  (/ (exp a) (+ (exp a) (exp b))))