Average Error: 0.6 → 0.6
Time: 40.2s
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 r48886007 = a;
        double r48886008 = exp(r48886007);
        double r48886009 = b;
        double r48886010 = exp(r48886009);
        double r48886011 = r48886008 + r48886010;
        double r48886012 = r48886008 / r48886011;
        return r48886012;
}
↓
double f(double a, double b) {
        double r48886013 = a;
        double r48886014 = exp(r48886013);
        double r48886015 = b;
        double r48886016 = exp(r48886015);
        double r48886017 = r48886014 + r48886016;
        double r48886018 = r48886014 / r48886017;
        return r48886018;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.0
Herbie0.6
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2019121 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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