Average Error: 0.7 → 0.6
Time: 10.1s
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 r5733600 = a;
        double r5733601 = exp(r5733600);
        double r5733602 = b;
        double r5733603 = exp(r5733602);
        double r5733604 = r5733601 + r5733603;
        double r5733605 = r5733601 / r5733604;
        return r5733605;
}
↓
double f(double a, double b) {
        double r5733606 = a;
        double r5733607 = exp(r5733606);
        double r5733608 = b;
        double r5733609 = exp(r5733608);
        double r5733610 = r5733607 + r5733609;
        double r5733611 = log(r5733610);
        double r5733612 = r5733606 - r5733611;
        double r5733613 = exp(r5733612);
        return r5733613;
}

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 2019170 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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