Average Error: 0.7 → 0.5
Time: 9.3s
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 r5315578 = a;
        double r5315579 = exp(r5315578);
        double r5315580 = b;
        double r5315581 = exp(r5315580);
        double r5315582 = r5315579 + r5315581;
        double r5315583 = r5315579 / r5315582;
        return r5315583;
}
↓
double f(double a, double b) {
        double r5315584 = a;
        double r5315585 = exp(r5315584);
        double r5315586 = b;
        double r5315587 = exp(r5315586);
        double r5315588 = r5315585 + r5315587;
        double r5315589 = log(r5315588);
        double r5315590 = r5315584 - r5315589;
        double r5315591 = exp(r5315590);
        return r5315591;
}

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

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-exp0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019135 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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