Average Error: 0.7 → 0.7
Time: 9.9s
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 r5448776 = a;
        double r5448777 = exp(r5448776);
        double r5448778 = b;
        double r5448779 = exp(r5448778);
        double r5448780 = r5448777 + r5448779;
        double r5448781 = r5448777 / r5448780;
        return r5448781;
}
↓
double f(double a, double b) {
        double r5448782 = a;
        double r5448783 = exp(r5448782);
        double r5448784 = b;
        double r5448785 = exp(r5448784);
        double r5448786 = r5448783 + r5448785;
        double r5448787 = r5448783 / r5448786;
        return r5448787;
}

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 2019151 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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