Average Error: 0.6 → 0.6
Time: 7.7s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{a - \log \left(e^{a} + e^{b}\right)}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{a - \log \left(e^{a} + e^{b}\right)}
double f(double a, double b) {
        double r114036 = a;
        double r114037 = exp(r114036);
        double r114038 = b;
        double r114039 = exp(r114038);
        double r114040 = r114037 + r114039;
        double r114041 = r114037 / r114040;
        return r114041;
}
↓
double f(double a, double b) {
        double r114042 = a;
        double r114043 = exp(r114042);
        double r114044 = b;
        double r114045 = exp(r114044);
        double r114046 = r114043 + r114045;
        double r114047 = log(r114046);
        double r114048 = r114042 - r114047;
        double r114049 = exp(r114048);
        return r114049;
}

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. Using strategy rm

  3. Applied add-exp-log0.6

    \[\leadsto \frac{e^{a}}{\color{blue}{e^{\log \left(e^{a} + e^{b}\right)}}}\]

  4. Applied div-exp0.6

    \[\leadsto \color{blue}{e^{a - \log \left(e^{a} + e^{b}\right)}}\]

  5. Simplified0.6

    \[\leadsto e^{\color{blue}{a - \log \left(e^{b} + e^{a}\right)}}\]

  6. Final simplification0.6

    \[\leadsto e^{a - \log \left(e^{a} + e^{b}\right)}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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