Average Error: 0.7 → 0.7
Time: 11.3s
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 r3898235 = a;
        double r3898236 = exp(r3898235);
        double r3898237 = b;
        double r3898238 = exp(r3898237);
        double r3898239 = r3898236 + r3898238;
        double r3898240 = r3898236 / r3898239;
        return r3898240;
}
↓
double f(double a, double b) {
        double r3898241 = a;
        double r3898242 = exp(r3898241);
        double r3898243 = b;
        double r3898244 = exp(r3898243);
        double r3898245 = r3898242 + r3898244;
        double r3898246 = r3898242 / r3898245;
        return r3898246;
}

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 2019151 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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