Average Error: 0.6 → 0.5
Time: 40.2s
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 r17872655 = a;
        double r17872656 = exp(r17872655);
        double r17872657 = b;
        double r17872658 = exp(r17872657);
        double r17872659 = r17872656 + r17872658;
        double r17872660 = r17872656 / r17872659;
        return r17872660;
}
↓
double f(double a, double b) {
        double r17872661 = a;
        double r17872662 = exp(r17872661);
        double r17872663 = b;
        double r17872664 = exp(r17872663);
        double r17872665 = r17872662 + r17872664;
        double r17872666 = log(r17872665);
        double r17872667 = r17872661 - r17872666;
        double r17872668 = exp(r17872667);
        return r17872668;
}

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 2019104 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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