Average Error: 0.7 → 0.7
Time: 14.5s
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 r7287679 = a;
        double r7287680 = exp(r7287679);
        double r7287681 = b;
        double r7287682 = exp(r7287681);
        double r7287683 = r7287680 + r7287682;
        double r7287684 = r7287680 / r7287683;
        return r7287684;
}
↓
double f(double a, double b) {
        double r7287685 = a;
        double r7287686 = exp(r7287685);
        double r7287687 = b;
        double r7287688 = exp(r7287687);
        double r7287689 = r7287686 + r7287688;
        double r7287690 = r7287686 / r7287689;
        return r7287690;
}

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. Final simplification0.7

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

Reproduce

herbie shell --seed 2019174 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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