Average Error: 0.7 → 0.6
Time: 12.8s
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 r3625786 = a;
        double r3625787 = exp(r3625786);
        double r3625788 = b;
        double r3625789 = exp(r3625788);
        double r3625790 = r3625787 + r3625789;
        double r3625791 = r3625787 / r3625790;
        return r3625791;
}
↓
double f(double a, double b) {
        double r3625792 = a;
        double r3625793 = exp(r3625792);
        double r3625794 = b;
        double r3625795 = exp(r3625794);
        double r3625796 = r3625793 + r3625795;
        double r3625797 = log(r3625796);
        double r3625798 = r3625792 - r3625797;
        double r3625799 = exp(r3625798);
        return r3625799;
}

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
Herbie0.6
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

    \[\frac{e^{a}}{e^{a} + e^{b}}\]
  2. Using strategy rm

  3. Applied add-exp-log0.7

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

  4. Applied div-exp0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019129 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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