Average Error: 0.5 → 0.5
Time: 12.2s
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 r69701 = a;
        double r69702 = exp(r69701);
        double r69703 = b;
        double r69704 = exp(r69703);
        double r69705 = r69702 + r69704;
        double r69706 = r69702 / r69705;
        return r69706;
}
↓
double f(double a, double b) {
        double r69707 = a;
        double r69708 = exp(r69707);
        double r69709 = b;
        double r69710 = exp(r69709);
        double r69711 = r69708 + r69710;
        double r69712 = r69708 / r69711;
        return r69712;
}

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 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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