Average Error: 0.7 → 0.7
Time: 14.4s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}
double f(double a, double b) {
        double r5044868 = a;
        double r5044869 = exp(r5044868);
        double r5044870 = b;
        double r5044871 = exp(r5044870);
        double r5044872 = r5044869 + r5044871;
        double r5044873 = r5044869 / r5044872;
        return r5044873;
}
↓
double f(double a, double b) {
        double r5044874 = a;
        double r5044875 = exp(r5044874);
        double r5044876 = b;
        double r5044877 = exp(r5044876);
        double r5044878 = r5044875 + r5044877;
        double r5044879 = r5044875 / r5044878;
        return r5044879;
}

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
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

    \[\frac{e^{a}}{e^{a} + e^{b}}\]

  2. Taylor expanded around inf 0.7

    \[\leadsto \color{blue}{\frac{e^{a}}{e^{b} + e^{a}}}\]

  3. Final simplification0.7

    \[\leadsto \frac{e^{a}}{e^{a} + e^{b}}\]

Reproduce

herbie shell --seed 2019149 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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