Average Error: 0.6 → 0.6
Time: 10.3s
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 r5237560 = a;
        double r5237561 = exp(r5237560);
        double r5237562 = b;
        double r5237563 = exp(r5237562);
        double r5237564 = r5237561 + r5237563;
        double r5237565 = r5237561 / r5237564;
        return r5237565;
}
↓
double f(double a, double b) {
        double r5237566 = a;
        double r5237567 = exp(r5237566);
        double r5237568 = b;
        double r5237569 = exp(r5237568);
        double r5237570 = r5237567 + r5237569;
        double r5237571 = r5237567 / r5237570;
        return r5237571;
}

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))))