Average Error: 0.7 → 0.7
Time: 16.3s
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 r9511228 = a;
        double r9511229 = exp(r9511228);
        double r9511230 = b;
        double r9511231 = exp(r9511230);
        double r9511232 = r9511229 + r9511231;
        double r9511233 = r9511229 / r9511232;
        return r9511233;
}
↓
double f(double a, double b) {
        double r9511234 = a;
        double r9511235 = exp(r9511234);
        double r9511236 = b;
        double r9511237 = exp(r9511236);
        double r9511238 = r9511235 + r9511237;
        double r9511239 = r9511235 / r9511238;
        return r9511239;
}

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 2019174 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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