Average Error: 0.6 → 0.6
Time: 11.1s
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 r3987289 = a;
        double r3987290 = exp(r3987289);
        double r3987291 = b;
        double r3987292 = exp(r3987291);
        double r3987293 = r3987290 + r3987292;
        double r3987294 = r3987290 / r3987293;
        return r3987294;
}
↓
double f(double a, double b) {
        double r3987295 = a;
        double r3987296 = exp(r3987295);
        double r3987297 = b;
        double r3987298 = exp(r3987297);
        double r3987299 = r3987296 + r3987298;
        double r3987300 = r3987296 / r3987299;
        return r3987300;
}

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
Herbie0.6
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  2. Taylor expanded around inf 0.6

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

  3. Final simplification0.6

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

Reproduce

herbie shell --seed 2019133 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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