Average Error: 0.7 → 0.7
Time: 14.9s
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 r5269004 = a;
        double r5269005 = exp(r5269004);
        double r5269006 = b;
        double r5269007 = exp(r5269006);
        double r5269008 = r5269005 + r5269007;
        double r5269009 = r5269005 / r5269008;
        return r5269009;
}
↓
double f(double a, double b) {
        double r5269010 = a;
        double r5269011 = exp(r5269010);
        double r5269012 = b;
        double r5269013 = exp(r5269012);
        double r5269014 = r5269011 + r5269013;
        double r5269015 = r5269011 / r5269014;
        return r5269015;
}

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 2019144 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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