Average Error: 0.7 → 0.7
Time: 14.3s
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 r7750929 = a;
        double r7750930 = exp(r7750929);
        double r7750931 = b;
        double r7750932 = exp(r7750931);
        double r7750933 = r7750930 + r7750932;
        double r7750934 = r7750930 / r7750933;
        return r7750934;
}
↓
double f(double a, double b) {
        double r7750935 = a;
        double r7750936 = exp(r7750935);
        double r7750937 = b;
        double r7750938 = exp(r7750937);
        double r7750939 = r7750936 + r7750938;
        double r7750940 = r7750936 / r7750939;
        return r7750940;
}

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 2019163 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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