Average Error: 0.5 → 0.5
Time: 15.8s
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 r98726 = a;
        double r98727 = exp(r98726);
        double r98728 = b;
        double r98729 = exp(r98728);
        double r98730 = r98727 + r98729;
        double r98731 = r98727 / r98730;
        return r98731;
}
↓
double f(double a, double b) {
        double r98732 = a;
        double r98733 = exp(r98732);
        double r98734 = b;
        double r98735 = exp(r98734);
        double r98736 = r98733 + r98735;
        double r98737 = r98733 / r98736;
        return r98737;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.5
Target0.0
Herbie0.5
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.5

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

  2. Final simplification0.5

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

Reproduce

herbie shell --seed 2019303 +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))))