Average Error: 0.6 → 0.6
Time: 6.9s
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 r156558 = a;
        double r156559 = exp(r156558);
        double r156560 = b;
        double r156561 = exp(r156560);
        double r156562 = r156559 + r156561;
        double r156563 = r156559 / r156562;
        return r156563;
}
↓
double f(double a, double b) {
        double r156564 = a;
        double r156565 = exp(r156564);
        double r156566 = b;
        double r156567 = exp(r156566);
        double r156568 = r156565 + r156567;
        double r156569 = r156565 / r156568;
        return r156569;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.0
Herbie0.6
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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