Average Error: 0.7 → 0.6
Time: 9.0s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{\sqrt[3]{\left(\left(a - \log \left(e^{a} + e^{b}\right)\right) \cdot \left(a - \log \left(e^{a} + e^{b}\right)\right)\right) \cdot \left(a - \log \left(e^{a} + e^{b}\right)\right)}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{\sqrt[3]{\left(\left(a - \log \left(e^{a} + e^{b}\right)\right) \cdot \left(a - \log \left(e^{a} + e^{b}\right)\right)\right) \cdot \left(a - \log \left(e^{a} + e^{b}\right)\right)}}
double f(double a, double b) {
        double r1327874 = a;
        double r1327875 = exp(r1327874);
        double r1327876 = b;
        double r1327877 = exp(r1327876);
        double r1327878 = r1327875 + r1327877;
        double r1327879 = r1327875 / r1327878;
        return r1327879;
}
↓
double f(double a, double b) {
        double r1327880 = a;
        double r1327881 = exp(r1327880);
        double r1327882 = b;
        double r1327883 = exp(r1327882);
        double r1327884 = r1327881 + r1327883;
        double r1327885 = log(r1327884);
        double r1327886 = r1327880 - r1327885;
        double r1327887 = r1327886 * r1327886;
        double r1327888 = r1327887 * r1327886;
        double r1327889 = cbrt(r1327888);
        double r1327890 = exp(r1327889);
        return r1327890;
}

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. Using strategy rm

  6. Applied add-cbrt-cube0.6

    \[\leadsto e^{\color{blue}{\sqrt[3]{\left(\left(a - \log \left(e^{a} + e^{b}\right)\right) \cdot \left(a - \log \left(e^{a} + e^{b}\right)\right)\right) \cdot \left(a - \log \left(e^{a} + e^{b}\right)\right)}}}\]

  7. Final simplification0.6

    \[\leadsto e^{\sqrt[3]{\left(\left(a - \log \left(e^{a} + e^{b}\right)\right) \cdot \left(a - \log \left(e^{a} + e^{b}\right)\right)\right) \cdot \left(a - \log \left(e^{a} + e^{b}\right)\right)}}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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