Average Error: 0.7 → 0.7
Time: 11.0s
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 r104267 = a;
        double r104268 = exp(r104267);
        double r104269 = b;
        double r104270 = exp(r104269);
        double r104271 = r104268 + r104270;
        double r104272 = r104268 / r104271;
        return r104272;
}
↓
double f(double a, double b) {
        double r104273 = a;
        double r104274 = exp(r104273);
        double r104275 = b;
        double r104276 = exp(r104275);
        double r104277 = r104274 + r104276;
        double r104278 = r104274 / r104277;
        return r104278;
}

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 2019212 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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