Average Error: 0.7 → 0.7
Time: 14.5s
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 r13094761 = a;
        double r13094762 = exp(r13094761);
        double r13094763 = b;
        double r13094764 = exp(r13094763);
        double r13094765 = r13094762 + r13094764;
        double r13094766 = r13094762 / r13094765;
        return r13094766;
}
↓
double f(double a, double b) {
        double r13094767 = a;
        double r13094768 = exp(r13094767);
        double r13094769 = b;
        double r13094770 = exp(r13094769);
        double r13094771 = r13094768 + r13094770;
        double r13094772 = r13094768 / r13094771;
        return r13094772;
}

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 2019173 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

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