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 r12876995 = a;
        double r12876996 = exp(r12876995);
        double r12876997 = b;
        double r12876998 = exp(r12876997);
        double r12876999 = r12876996 + r12876998;
        double r12877000 = r12876996 / r12876999;
        return r12877000;
}
↓
double f(double a, double b) {
        double r12877001 = a;
        double r12877002 = exp(r12877001);
        double r12877003 = b;
        double r12877004 = exp(r12877003);
        double r12877005 = r12877002 + r12877004;
        double r12877006 = r12877002 / r12877005;
        return r12877006;
}

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 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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