Average Error: 0.7 → 0.7
Time: 15.4s
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 r4552045 = a;
        double r4552046 = exp(r4552045);
        double r4552047 = b;
        double r4552048 = exp(r4552047);
        double r4552049 = r4552046 + r4552048;
        double r4552050 = r4552046 / r4552049;
        return r4552050;
}
↓
double f(double a, double b) {
        double r4552051 = 1.0;
        double r4552052 = a;
        double r4552053 = exp(r4552052);
        double r4552054 = b;
        double r4552055 = exp(r4552054);
        double r4552056 = r4552053 + r4552055;
        double r4552057 = r4552056 / r4552053;
        double r4552058 = r4552051 / r4552057;
        return r4552058;
}

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))))