Average Error: 0.5 → 0.5
Time: 10.8s
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 r103832 = a;
        double r103833 = exp(r103832);
        double r103834 = b;
        double r103835 = exp(r103834);
        double r103836 = r103833 + r103835;
        double r103837 = r103833 / r103836;
        return r103837;
}
↓
double f(double a, double b) {
        double r103838 = a;
        double r103839 = exp(r103838);
        double r103840 = b;
        double r103841 = exp(r103840);
        double r103842 = r103839 + r103841;
        double r103843 = r103839 / r103842;
        return r103843;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.5
Target0.0
Herbie0.5
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.5

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

  2. Final simplification0.5

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

Reproduce

herbie shell --seed 2019303 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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