Average Error: 0.7 → 0.7
Time: 5.3s
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 r163050 = a;
        double r163051 = exp(r163050);
        double r163052 = b;
        double r163053 = exp(r163052);
        double r163054 = r163051 + r163053;
        double r163055 = r163051 / r163054;
        return r163055;
}
↓
double f(double a, double b) {
        double r163056 = 1.0;
        double r163057 = a;
        double r163058 = exp(r163057);
        double r163059 = b;
        double r163060 = exp(r163059);
        double r163061 = r163058 + r163060;
        double r163062 = r163061 / r163058;
        double r163063 = r163056 / r163062;
        return r163063;
}

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 2019356 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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