Average Error: 0.8 → 0.8
Time: 11.5s
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 r72005 = a;
        double r72006 = exp(r72005);
        double r72007 = b;
        double r72008 = exp(r72007);
        double r72009 = r72006 + r72008;
        double r72010 = r72006 / r72009;
        return r72010;
}
↓
double f(double a, double b) {
        double r72011 = a;
        double r72012 = exp(r72011);
        double r72013 = b;
        double r72014 = exp(r72013);
        double r72015 = r72012 + r72014;
        double r72016 = r72012 / r72015;
        return r72016;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.8
Target0.0
Herbie0.8
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.8

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

  2. Final simplification0.8

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

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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