Average Error: 0.7 → 0.7
Time: 2.5s
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 r163261 = a;
        double r163262 = exp(r163261);
        double r163263 = b;
        double r163264 = exp(r163263);
        double r163265 = r163262 + r163264;
        double r163266 = r163262 / r163265;
        return r163266;
}
↓
double f(double a, double b) {
        double r163267 = a;
        double r163268 = exp(r163267);
        double r163269 = b;
        double r163270 = exp(r163269);
        double r163271 = r163268 + r163270;
        double r163272 = r163268 / r163271;
        return r163272;
}

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 2020057 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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