Average Error: 0.7 → 0.7
Time: 14.9s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}
double f(double a, double b) {
        double r6708623 = a;
        double r6708624 = exp(r6708623);
        double r6708625 = b;
        double r6708626 = exp(r6708625);
        double r6708627 = r6708624 + r6708626;
        double r6708628 = r6708624 / r6708627;
        return r6708628;
}
↓
double f(double a, double b) {
        double r6708629 = 1.0;
        double r6708630 = a;
        double r6708631 = exp(r6708630);
        double r6708632 = b;
        double r6708633 = exp(r6708632);
        double r6708634 = r6708631 + r6708633;
        double r6708635 = r6708634 / r6708631;
        double r6708636 = r6708629 / r6708635;
        return r6708636;
}

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. Using strategy rm

  3. Applied clear-num0.7

    \[\leadsto \color{blue}{\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}}\]

  4. Final simplification0.7

    \[\leadsto \frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

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