Average Error: 0.6 → 0.5
Time: 16.1s
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 r4429906 = a;
        double r4429907 = exp(r4429906);
        double r4429908 = b;
        double r4429909 = exp(r4429908);
        double r4429910 = r4429907 + r4429909;
        double r4429911 = r4429907 / r4429910;
        return r4429911;
}
↓
double f(double a, double b) {
        double r4429912 = a;
        double r4429913 = exp(r4429912);
        double r4429914 = b;
        double r4429915 = exp(r4429914);
        double r4429916 = r4429913 + r4429915;
        double r4429917 = log(r4429916);
        double r4429918 = r4429912 - r4429917;
        double r4429919 = exp(r4429918);
        return r4429919;
}

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

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-exp0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019158 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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