Average Error: 0.6 → 0.6
Time: 13.7s
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 r84023 = a;
        double r84024 = exp(r84023);
        double r84025 = b;
        double r84026 = exp(r84025);
        double r84027 = r84024 + r84026;
        double r84028 = r84024 / r84027;
        return r84028;
}
↓
double f(double a, double b) {
        double r84029 = a;
        double r84030 = exp(r84029);
        double r84031 = b;
        double r84032 = exp(r84031);
        double r84033 = r84030 + r84032;
        double r84034 = r84030 / r84033;
        return r84034;
}

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 2019209 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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