Average Error: 0.6 → 0.6
Time: 10.1s
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 r6170235 = a;
        double r6170236 = exp(r6170235);
        double r6170237 = b;
        double r6170238 = exp(r6170237);
        double r6170239 = r6170236 + r6170238;
        double r6170240 = r6170236 / r6170239;
        return r6170240;
}
↓
double f(double a, double b) {
        double r6170241 = a;
        double r6170242 = exp(r6170241);
        double r6170243 = b;
        double r6170244 = exp(r6170243);
        double r6170245 = r6170242 + r6170244;
        double r6170246 = r6170242 / r6170245;
        return r6170246;
}

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 2019172 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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