Average Error: 0.8 → 0.7
Time: 10.0s
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 r5294812 = a;
        double r5294813 = exp(r5294812);
        double r5294814 = b;
        double r5294815 = exp(r5294814);
        double r5294816 = r5294813 + r5294815;
        double r5294817 = r5294813 / r5294816;
        return r5294817;
}
↓
double f(double a, double b) {
        double r5294818 = a;
        double r5294819 = exp(r5294818);
        double r5294820 = b;
        double r5294821 = exp(r5294820);
        double r5294822 = r5294819 + r5294821;
        double r5294823 = log(r5294822);
        double r5294824 = r5294818 - r5294823;
        double r5294825 = exp(r5294824);
        return r5294825;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.8
Target0.0
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.8

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

  3. Applied add-exp-log0.8

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

  4. Applied div-exp0.7

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

  5. Final simplification0.7

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

Reproduce

herbie shell --seed 2019152 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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