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 r5584925 = a;
        double r5584926 = exp(r5584925);
        double r5584927 = b;
        double r5584928 = exp(r5584927);
        double r5584929 = r5584926 + r5584928;
        double r5584930 = r5584926 / r5584929;
        return r5584930;
}
↓
double f(double a, double b) {
        double r5584931 = a;
        double r5584932 = exp(r5584931);
        double r5584933 = b;
        double r5584934 = exp(r5584933);
        double r5584935 = r5584932 + r5584934;
        double r5584936 = log(r5584935);
        double r5584937 = r5584931 - r5584936;
        double r5584938 = exp(r5584937);
        return r5584938;
}

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 2019192 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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