Average Error: 0.7 → 0.7
Time: 10.0s
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 r2552922 = a;
        double r2552923 = exp(r2552922);
        double r2552924 = b;
        double r2552925 = exp(r2552924);
        double r2552926 = r2552923 + r2552925;
        double r2552927 = r2552923 / r2552926;
        return r2552927;
}
↓
double f(double a, double b) {
        double r2552928 = a;
        double r2552929 = exp(r2552928);
        double r2552930 = b;
        double r2552931 = exp(r2552930);
        double r2552932 = r2552929 + r2552931;
        double r2552933 = r2552929 / r2552932;
        return r2552933;
}

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 2019128 +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))))